Tower's view

From the church tower's view at the height of 65 m, the top of the house can be seen at a depth angle of alpha = 45° and its bottom at a depth angle of beta = 58°. Calculate the height of the house and its distance from the church.

Correct answer:

y =  24.3835 m
x =  40.6165 m

Step-by-step explanation:

$$\begin{gathered} h=65\text{ m } \\ \alpha =45^{\circ } \\ \beta =58^{\circ } \\ \tan \beta =h:x \\ x=h\mathrm{/}\tan {\beta }^{\circ }=h\mathrm{/}\tan 58^{\circ }=65\mathrm{/}\tan 58^{\circ }=65\mathrm{/}1.600335=40.61651\text{ m } \\ \tan \alpha =(h-y):x \\ y=h-x\cdot \tan {\alpha }^{\circ }=h-x\cdot \tan 45^{\circ }=65-40.6165\cdot \tan 45^{\circ }=65-40.6165\cdot 1=24.383=24.3835\text{ m} \end{gathered}$$

$x=40.6165\text{ m}$

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