NEED HELP ASAP WILL GIVE BRAINLY PLEASE I NEED THIS

Mathematics

1 answer:

Eddi Din [679]3 years ago

4 0

Bmrruray is the answer

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Mike wants to work out the height of a tree which has a fence around it. From A he sees that the angle of elevation of the top i

larisa [96]

Answer: 13.8 m

Step-by-step explanation:

Given

From point A, angle of elevation is $19^{\circ}$

From point B which is 18 m closer, it changes to $32^{\circ}$

Suppose the height of tree is h

From figure, we can write

$\Rightarrow \tan 32=\dfrac{h}{x}\\\\\Rightarrow h=x\tan 32^{\circ}$

Similarly

$\Rightarrow \tan19^{\circ}=\dfrac{h}{x+18}\\\\\Rightarrow h=(x+18)\tan 19^{\circ}\\\text{Substitute the value of h}\\\Rightarrow x\tan 32^{\circ}=x\tan 19^{\circ}+18\tan 19^{\circ}\\\Rightarrow x(\tan32^{\circ}-\tan 19^{\circ})=18\tan 19^{\circ}\\\\\Rightarrow x=\dfrac{18\tan 19^{\circ}}{\tan32^{\circ}-\tan 19^{\circ}}\\\\\Rightarrow x=22.09\approx 22.1\ m$