Which of the following values best approximates of the length of c in triangle ABC where c = 90(degrees), b = 12, and B = 15(degrees)?
c = 3.1058
c = 12.4233
c = 44.7846
c = 46.3644
In triangle ABC, find b, to the nearest degree, given a = 7, b = 10, and C is a right angle.
35(degrees)
44(degrees)
46(degrees)
55(degrees)
Solve the right triangle ABC with right angle C if B = 30(degrees) and c = 10.
a = 5, b = 5, A = 60(degrees)
a = 5, b = 8.6602, A = 60(degrees)
a = 5.7735, b = 11.5470, A = 60(degrees)
a = 8.6602, b = 5, A = 60(degrees)
I'm horrible at trig and I do not know how to do this, please help?
To find the length of side c in triangle ABC, we can use the Law of Sines, which states that in any triangle, the ratio of the length of a side to the sine of its opposite angle is constant.
In our case, we can use the following formula:
c/sin(C) = b/sin(B)
Given that C=90 degrees, b=12, and B=15 degrees, we can substitute these values into the formula and solve for c:
c/sin(90) = 12/sin(15)
Since sin(90) = 1, the equation simplifies to:
c/1 = 12/sin(15)
Now we can solve for c:
c = 12/sin(15)
To find the approximate value of c, we need to evaluate sin(15) using a calculator:
sin(15) ≈ 0.2588
Substituting this back into the equation:
c = 12/0.2588
c ≈ 46.3644
Therefore, the value that best approximates the length of c in triangle ABC is c = 46.3644.
Now, let's move on to the next question:
To find the value of angle B in triangle ABC, we can use the inverse sine function (sin^-1) since we are given the length of sides a and b and the measure of angle C, which is a right angle (90 degrees).
Using the formula: sin(B) = b/a
Given that a = 7 and b = 10, we can substitute these values into the formula and solve for B:
sin(B) = 10/7
Using a calculator, we can find the inverse sine of this value:
B ≈ sin^-1(10/7) ≈ 44.83 degrees
Rounded to the nearest degree, B ≈ 45 degrees.
Therefore, the value of angle B, to the nearest degree, is 45 degrees.
Moving on to the last question:
To solve the right triangle ABC with angle C as the right angle, B = 30 degrees, and c = 10, we can use the trigonometric functions sine, cosine, and tangent.
Given that c = 10, we can find side a using the equation: sin(B) = a/c
sin(30) = a/10
Using a calculator, we find that sin(30) ≈ 0.5, so the equation becomes:
0.5 = a/10
Multiplying both sides by 10, we get:
a = 5
Next, we can use the Pythagorean theorem to find side b:
a^2 + b^2 = c^2
Substituting the known values:
5^2 + b^2 = 10^2
25 + b^2 = 100
Subtracting 25 from both sides:
b^2 = 75
Taking the square root of both sides:
b ≈ √75 ≈ √(25 * 3) ≈ 5√3 ≈ 8.6602
Therefore, the values that approximate the lengths of sides a, b, and the measure of angle A in triangle ABC are:
a = 5, b ≈ 8.6602, A = 60 degrees.
I hope this helps! Let me know if you have any further questions.
To solve these trigonometry problems, you can use different trigonometric ratios such as sine, cosine, and tangent. Here's how you can solve each of the given problems step by step:
1) Approximating the Length of c in Triangle ABC:
To find the length of side c, you can use the sine ratio:
sin(C) = opposite/hypotenuse
In this case, sin(C) = opposite/12
Since C = 90 degrees, sin(C) = sin(90) = 1
So we can write: 1 = opposite/12
Rearranging the equation, we get: opposite = 12
Therefore, the length of side c is 12.
2) Finding b in Triangle ABC:
To find the value of angle B, you can use the sine ratio:
sin(B) = opposite/hypotenuse
In this case, sin(B) = opposite/10
Since B = 90 degrees, sin(B) = sin(90) = 1
So we can write: 1 = opposite/10
Rearranging the equation, we get: opposite = 10
Therefore, the length of side b is 10.
3) Solving the Right Triangle ABC:
To find the other sides and angles of the triangle, you can use different trigonometric ratios depending on the given information.
Given: B = 30 degrees and c = 10.
Using the sine ratio for angle B:
sin(B) = opposite/hypotenuse
sin(30) = opposite/10
opposite = 10 * sin(30) = 10 * 0.5 = 5
Using the cosine ratio for angle B:
cos(B) = adjacent/hypotenuse
cos(30) = adjacent/10
adjacent = 10 * cos(30) = 10 * (√3/2) = 5√3
Now, you can use the Pythagorean theorem to find the length of the remaining side:
a^2 + b^2 = c^2
a^2 + (5√3)^2 = 10^2
a^2 + 75 = 100
a^2 = 100 - 75
a^2 = 25
a = √25 = 5
Since the other given angle is right angle C, which is 90 degrees, the remaining angle A can be found:
A = 180 - B - C
A = 180 - 30 - 90
A = 60 degrees
Therefore, in this right triangle ABC, the values are:
a = 5, b = 5√3, A = 60 degrees.
I hope this explanation helps you understand how to solve these trigonometry problems step by step.
"I am horrible at trig" is a cop-out.
All you have to remember in a right-angled triangle is 3 pairs of sides combinations for the primary trig functions.
Memorize the following word: SOH-CAH-TOA
SOH -- SinØ = Opposite/Hypotenuse , not the S,O, and H
CAH --CosØ = Adjacent/Hypotenus
TOA -- TanØ = Opposite/Hypotenuse
The other notation you should know that in labeling triangles, capital letters are usually used for the angles and small letters would be the sides opposite those angles.
Draw a right-angled triangle ABC, label it that way, and MEMORIZE the above, you are "horrible" at it only because you have not made the effort to learn this.
The first one:
Which of the following values best approximates of the length of c in triangle ABC where C = 90°, b = 12, and B = 15° ? (notice c ---> C, since C is an angle)
So in terms of the 15° angle , b is the Opposite and c is the Hypotenuse
so "opposite - hypotenuse" form SOH-CAH-TOA suggests sin
sin 15° = 12/c
c sin15 = 12
c = 12/sin15° = 46.3644
after doing a few, you can do each in 3 or less lines
#2, this time you are not given any angles, but you are given 2 sides
"In triangle ABC, find B, to the nearest degree, given a = 7, b = 10, and C is a right angle. " (notice I changed b --> B)
make your sketch , in terms of angle B, we are given the opposite and the adjacent, so that suggests tan
tanB = 10/7 = ....
B = 55° , see that? only 2 lines of actual work
(on my calculator, I did the following:
10÷7 =
2ndF
tan
=
and I got 55.0079.... )
try the rest, they are easy
by solving a triangle, you are finding all the missing sides and missing angles.
remember, in a right-angles triangle as soon as you have one of the smaller angle, you also have the third since their sum must be 90°
Also if you have 2 sides in a right-angled triangle you could also find the third by Pythagoras. This is often a good way to check your answers.