trigonometry easy..

Algebra Level 2

Linda measures the angle of elevation from a point on the ground to the top of the tree and find it to be 35degrees. She then walks 20 meters towards the tree and finds the angle of elevation from this new point to the top of the tree to be 45 degress. Find the height of the tree. (Round answer to three significant digits).


The answer is 46.7.

Edil Tizon by edil tizon , 23, Philippines

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2 solutions

By sine law, we have

x sin ⁡ 35 = 20 sin ⁡ 10 \dfrac{x}{\sin~35}=\dfrac{20}{\sin~10} ⟹ \implies x ≈ 66.06 x \approx 66.06

By pythagorean theorem, we have

sin ⁡ 45 = h 66.06 \sin~45=\dfrac{h}{66.06}

h = 46.71 \color{#D61F06}\boxed{h=46.71}

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Edil Tizon
Feb 5, 2015

tan(35 degrees) = h / x and tan(45degrees) = h / (x - 20) , where h is the height of the tree.

Solve both equations for x to find

x = h / tan(35degrees) and x = h / tan(45degrees) + 20

Which gives h / tan(35degrees) = h / tan(45degrees) + 20

Solve for h; h = [ 20 tan(35degrees) tan(45degrees) ] / [ tan(45degrees) - tan(35degrees) ] = 46.7 meters (3 significant digits) final answer=46.7

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