In a right triangle sinA= 3/5 and C=17. Find a and b.
Be sure to draw a right triangle and letter it properly.
how can i solve the math in this problem. i know i would have to use the Pythagoream Theorem but i don't know how to set the problem up first.
SinA= b/C=3/4
you are given C, so b= 3/4 * 17
then a can be found from a^2+b^2=C^2
your question makes no sense
If you have a right-angled triangle where
sinA = 3/5, then the opposite side to vertex A is 3 and the hypotenuse is 5,
by Pythagoras it is easy to show that the third side is 4
(you should have recognized the 3-4-5 right-angled triangle)
if sinA = 3/5, then angle A is appro 37.9°
what does C=17 mean?
sinA= 3/5 and C=17
Finding a and b
would this work as an answer ..?
sinA = opp/hyp = a/c = 3/5 = 3*3.4/5*3.4 = 10.2/17
a = 10.2
Applying Pythagoream Theorem a^2 + b^2 = c^2
b= sqrt 17^2 - 10.2^2 = 13.6
??
To solve this problem, we can start by drawing a right triangle and labeling it properly. Let's label the three sides as follows:
- The side opposite angle A: a
- The side adjacent to angle A: b
- The hypotenuse: c
Since we have sinA = 3/5, we know that the ratio of the opposite side to the hypotenuse is 3/5. Therefore, we can write:
sinA = a/c = 3/5
We also know that c = 17. Now, we can set up an equation using the Pythagorean Theorem:
a^2 + b^2 = c^2
Substituting the value of c, we get:
a^2 + b^2 = 17^2
Now, let's solve for a and b:
Rearranging the equation, we have:
a^2 = 17^2 - b^2
Now, let's substitute the value of sinA into the equation:
(3/5)^2 = 17^2 - b^2
Simplifying, we have:
9/25 = 289 - b^2
To solve for b, we can subtract 289 from both sides:
b^2 = 289 - (9/25)
Now, let's calculate the value of b^2:
b^2 = (289 * 25 - 9) / 25
b^2 = (7225 - 9) / 25
b^2 = 7216 / 25
To find b, we can take the square root of both sides:
b = √(7216 / 25)
b ≈ 13.52
Now, let's solve for a:
a^2 = 17^2 - b^2
a^2 = 289 - 13.52^2
a^2 = 289 - 182.6304
a^2 ≈ 106.3696
Taking the square root of both sides:
a ≈ √106.3696
a ≈ 10.31
Therefore, a ≈ 10.31 and b ≈ 13.52.