If m = 90 ° and m = 35 ° , one would use sin A to find the value of b .

Question

If m  = 90 ° and m  = 35 ° , one would use sin A to find the value of b .

Quizplus · Accepted Answer

If we draw a right triangle with angle A = 90° and angle B = 35°, then angle C = 55° (since the angles of a triangle add up to 180°). Let b be the length of the side opposite angle B. Then, we can use the sine function to find b:

sin B = opposite/hypotenuse
sin 35° = b/hypotenuse

We can solve for hypotenuse:

hypotenuse = b/sin 35°

Now, we need to find the length of the side adjacent to angle B, which we can call a. We can use the angle sum property of triangles to find angle A:

angle A = 180° - angle B - angle C
angle A = 180° - 35° - 55°
angle A = 90°

Since angle A is a right angle, the side opposite it (which we have been calling hypotenuse) is actually the hypotenuse of the triangle. Therefore, we can use the sine function again to relate the length of side a to the hypotenuse:

sin A = opposite/hypotenuse
sin 90° = a/hypotenuse
1 = a/hypotenuse

So, we have:

a = hypotenuse = b/sin 35°

Therefore, we can use sin A (which equals 1) to find b:

b/sin 35° = hypotenuse = a = b/1

Simplifying, we get:

b/sin 35° = b/1

Multiplying both sides by sin 35°, we get:

b = sin 35° * b/ sin 35°

Simplifying, we get:

b = 1 * b

Therefore, we have:

b = b

This is true for any value of b, so we don't need to know the specific value of angle A (which happens to be 90° in this case) in order to use sin A to find the value of b.

If M = 90 ° and M =