Question

13. Two points P and Q, 10 m apart on level ground,

are due West of the foot B of a tree TB. Given that
TPB = 23° and TQB = 32°, find the height of tree​

Answer 1

Answer: height = 13.24 m

Explanation:

Draw a picture (see image below), then set up the proportions to find the length of QB. Then input QB into either of the equations to find h.

Given: PQ = 10

∠TPB = 23°

∠TQB = 32°

`\tan P=(opposite)/(adjacent)\qquad \qquad \tan Q=(opposite)/(adjacent)\\\\\\\tan 23^o=(h)/(10+x)\qquad \qquad \tan 32^o=(h)/(x)\\\\\\\underline{\text{Solve each equation for h:}}\\\tan 23^o(10+x)=h\qquad \qquad \tan 32^o(x)=h\\\\\\\underline{\text{Set the equations equal to each other and solve for x:}}\\\tan23^o(10+x)=\tan32^o(x)\\0.4245(10+x)=0.6249x\\4.245+0.4245x=0.6249x\\4.245=0.2004x\\21.18=x`

`\underline{\text{In put x = 21.18 into either equation and solve for h:}}\\h=\tan 32^o(x)\\h=0.6249(2.118)\\\large\boxed{h=13.24}`