Question

two students stand 1 yard apart and measure their respective angles of elevation to the top of a tree. student a measures the angle to be 57°, and student b measures the angle to be 46°. what is h, the height of the tree? use the law of sines to first find at. then use that measure to find the value of h. law of sines: $\frac{sin(a)}{a}=\frac{sin(b)}{b}=\frac{sin(c)}{c}$

Explanation:

Step1: Find angle at T in △ATB

Angle at T = 180° - 123° - 46° = 11°

Step2: Apply Law of Sines to find AT

AT = AB·sin(46°)/sin(11°) ≈ 1·0.7193/0.1908 ≈ 3.77 yd

Step3: Calculate h using AT

h = AT·sin(57°) ≈ 3.77·0.8387 ≈ 3.2 yd

Answer:

B. 3.2 yards