You are watching: A tree on a hillside casts a shadow

I perform not understand exactly how to deal with this problem, any aid would be lot appreciated (note: ns do have the answer to the question, so the is the actions to accomplish that prize is what i am interested in) . Give thanks to you in advance!

First, attract a diagram.Second, try to find all of the missing angles. What is $52^\circ-22^\circ$?Next, use the trig definitions to uncover some the the absent sides. Among those political parties is the tree; come up with a strategy.

It seems that you understand the hypothenuse (215 ft)... So usage 215 ft x sin22 and also 215 ft x cos22 to discover the political parties of the ideal triangle... Then usage the base and also tan52 to discover the length of "215 ft sin22 + tree"... You room done...

Consider my absolutely horrible drawing. The sunlight is $55º $ the inclination end the horizontal. The hill is $22º$ of inclination end the horizontal. Thus the edge formed between the basic of the tree, the base of the hill and the sun is $55º-22º=33º.$ Now, consider the edge $\beta$. We understand that $\beta + 55º +90º = 180º \Rightarrow \beta = 35º$. Now use the legislation of sines:

$$\frac\sin 33ºh = \frac\sin\beta215 ft.$$

PD: Oops! I check out the edge of key of the sunlight was $55º$ rather of $52º$. Ns won"t re-draw. Just change everything in the procedure so the the angle of elevation is the correct one.

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