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# Franklin is standing 30 ft from the base of a building

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Franklin is standing 30 ft from the base of a building. The angle of elevation from his feet to the top of the building is 53°.

How tall is the building?

Netzer7  Jun 7, 2017

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Use the trigonometric ratios to find the height of the building:

 $$\frac{\tan 53}{1}=\frac{x}{30}$$ The tangent trigonometric ratio compares the opposite angle and the adjacent angle. Cross multiply to isolate x. $$30\tan 53ft=x$$ Use a calculator to approximate the height of the building $$30 \tan(53)\approx39.8113ft$$ Of course, leave units in your final answer!

One last note before you go!

Be sure that your calculator is in degree mode when doing this calculation!

TheXSquaredFactor  Jun 7, 2017
edited by TheXSquaredFactor  Jun 7, 2017
Sort:

#1
+1602
+2

Use the trigonometric ratios to find the height of the building:

 $$\frac{\tan 53}{1}=\frac{x}{30}$$ The tangent trigonometric ratio compares the opposite angle and the adjacent angle. Cross multiply to isolate x. $$30\tan 53ft=x$$ Use a calculator to approximate the height of the building $$30 \tan(53)\approx39.8113ft$$ Of course, leave units in your final answer!

One last note before you go!

Be sure that your calculator is in degree mode when doing this calculation!

TheXSquaredFactor  Jun 7, 2017
edited by TheXSquaredFactor  Jun 7, 2017

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