Suppose a triangle has angles A,B, and C. Angle C is the right angle. Find the measures of the other sides to the nearest whole number.
< means angle symbol.
1.BC=9,m<B=72 degrees
I got angle AB=28 and angle AC=29
To solve these problems you find either the sine, cosine, or tangent of the equation. Afterwards you just cross multiply. Well, when I went to check my work, the answers were flip flopped(AC=28 and AB=29). Can someone check my work to make sure I am right.
NEVER MIND I CHECKED IT AGAIN AND FOUND THE RIGHT ANSWERS
To solve for the measures of the other sides of the triangle, we need to use trigonometric ratios. In a right triangle, we have three trigonometric ratios: sine (sin), cosine (cos), and tangent (tan).
Let's start by identifying the sides of the triangle. In your case, let's consider BC as the base, AB as the height, and AC as the hypotenuse.
Given that BC = 9 and angle B = 72 degrees, we can use the sine ratio, which relates the opposite side (AB) to the hypotenuse (AC). The sine of an angle is equal to the ratio of the length of the opposite side to the length of the hypotenuse.
sin(B) = AB/AC
Rearranging the equation, we get:
AB = AC * sin(B)
Substituting the values, we have:
AB = AC * sin(72)
Now, we can solve for AB using a calculator or trigonometric table. After substituting the values, we find:
AB ≈ AC * 0.9511
Similarly, we can find AC using cosine ratio. The cosine of an angle is equal to the ratio of the length of the adjacent side (BC) to the length of the hypotenuse (AC).
cos(B) = BC/AC
Rearranging the equation, we get:
AC = BC/cos(B)
Substituting the values, we have:
AC = 9 / cos(72)
Now, we can solve for AC using a calculator or trigonometric table. After substituting the values, we find:
AC ≈ 9 / 0.3090
So, AC ≈ 29, rounded to the nearest whole number, and AB ≈ 28, also rounded to the nearest whole number.
As a result, the measures of the other sides to the nearest whole number are AB = 28 units and AC = 29 units.