Question

in triangle rst above, point w (not shown) lies on rt. what is the value of cos(∠rsw wst ) ( − sin ∠ ) ?

Answer 1

The value of cos(∠RSW − ∠WST) in triangle RST, with point W on RT, is 1.

Step-by-step explanation:

In triangle RST, point W lies on RT. We are asked to find the value of cos(∠RSW − ∠WST). To do this, we need to find the measure of both angles RSW and WST.

Since point W lies on RT, we can use the angle-side-angle (ASA) congruence condition. Angle RSW is congruent to angle RWT because they are vertical angles, and angle WST is congruent to angle WRT. Therefore, angle RSW is equal to angle RWT, and angle WST is equal to angle WRT.

Using the congruent angles, we can calculate the value of cos(∠RSW − ∠WST). Since angles RSW and WST are congruent, their difference is 0, so cos(∠RSW − ∠WST) = cos(0) = 1.