Which is closest to the value of w in the triangle below?

B. 2.5 in

Step-by-step explanation:

From the given right angle triangle,

the hypotenuse of the right angle triangle is the unknown side.

With m∠32 as the reference angle,

the adjacent side of the right angle triangle is 4 in

the opposite side of the right angle triangle is w

To determine w, we would apply

the tangent trigonometric ratio which is expressed as

Tan θ = opposite side/adjacent side. Therefore,

Tan 32 = w/4

w = 4tan32 = 4 × 0.625

w = 2.5 in

answer: option a.

step-by-step explanation:

you know that the quadrilateral opqr ( a four sided figure) is inscribed in circle. this means that all its vertices are on the circle.

then, by definition, the opposite angles of the quadrilateral are supplementary, this means that the sum of their measures is 180 degrees.

you can observe in the figure that the angles ∠opq   and the angle ∠orq   are opposite, therefore:

then, can be used to d to calculate the measure of ∠opq