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. 3.0 yards 3.2 yards 3.8 yards 4.4 yards law of sines: $\frac{sin(a)}{a}=\frac{sin(b)}{b}=\frac{sin(c)}{c}$

Explanation:

Step1: Find angles in triangle ABT

Angle at A: 180° - 57° = 123°, angle at B: 46°, angle at T: 180° - 123° - 46° = 11°

Step2: Apply law of sines to find AT

$\frac{AT}{\sin(46^\circ)} = \frac{1}{\sin(11^\circ)}$, so $AT = \frac{\sin(46^\circ)}{\sin(11^\circ)} \approx \frac{0.7193}{0.1908} \approx 3.77$ yards

Step3: Calculate h using AT

In right triangle AGT, $h = AT \cdot \sin(57^\circ) \approx 3.77 \cdot 0.8387 \approx 3.2$ yards

Answer:

B. 3.2 yards