Height of a Tree A tree top top a hillside casts a shadow215 ft under the hill. If the edge of inclination of thehillside is 22 to the horizontal and the angle of elevationof the sun is 52, uncover the height of the tree.

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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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