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the angle of elevation of the top of a tree is found to be 33 degrees at one point and 59 degrees at a point 31 ft nearer the tree. how high is the tree if both observation points and the base of the tree are in the same horizontal plane?

Sagot :

Shinalcantaraidn

Please refer to the attachment for the illustration.

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Using tangent you'll have:

[tex]tan59^0 = \frac{h}{x-31} \\ (x-31)tan59^0 = h ~~----equation1 \\ tan33^0 = \frac{h}{x} \\ xtan33^0 = h~~----equation2 \\ equate~1&2 \\ (x-31)tan59^0 = xtan33^0 \\ xtan59^0-31tan59^0 = xtan33^0 \\ xtan59^0 - xtan33^0 = 31tan59^0 \\ 1.01487x = 51.59266 \\ x = 50.8367 \\ ------------- \\ to~find~h~substitute~x~to~equation2 \\ xtan33^0 = h \\ (50.8367)tan33^0 = h \\ h = 33.01375ft.[/tex]

View image Shinalcantara