Question

Solve for the missing angle ∡&. One point for your equation and one point for the correct angle measure.

Answer 1

Hello.

1. Understand that this requires inverse trigonometry.
2. For A, we can use sin^-1 if we want (we could use cos^-1 or tan^-1 as well because all sides are given)
Definition of sin^-1 with how it is derived
sin(theta) = O/H <—> sin^-1(O/H)
Angle A: (When calculating an angle, ensure that your calculation is in degree mode instead of radian mode.) 2ND, then QUIT on TI

sin^-1(7/25) = 16.26020471°
(round as needed)

Angle &: (also in degree mode)

All angles of a triangle add to 180°.
1. 180° - (angle B + Angle A) = Angle &
2. 180° - (90° + 16.26020471°) = 73.73979529°
(round as needed)

To quickly check: 16° + 90° + 73° = 180°, as expected for a triangle

From the picture you provided,

The angle values make sense because that triangle represents a 30-60-90 degree triangle. (Also, a good trick is to know that the smallest angle of a triangle will always have the smallest side value, and the largest angle has the largest side value.)
Unless we have an equilateral triangle!

Good luck to you!