Question

Grace is standing 14 feet from a lighthouse and Kelly is standing 12 feet from Grace. The angle that Grace looks up to see the top of the lighthouse is 45°. The angle that Kelly looks up to see the top of the lighthouse is y°.
A.) Find the height, h, of the lighthouse.
B.) Find the angle, rounded to the nearest tenth of a degree, in which Kelly looks up to the top of the lighthouse.
C.) To the nearest tenth of a degree, find the value of x° . In two or more sentences, explain your calculations

Answer 1

To find the height of the lighthouse, use $tan45= \frac{h}{14}$ to get that h = 14 (the tangent of 45 is 1).  Now for the next question, you have to use the height you just solved for to find angle y.  Use $tan(y)= \frac{14}{26}$ and the inverse tangent button on your calculator tells us that the angle is 28.3. Now for the last question, use the supplement of 45 to get that the angle adjacent to y is 135.  180 - 135 - 28.3 = 16.7  That's your x value.