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Paraphin [41]
3 years ago
5

You are standing 40 meters from the base of a tree that leans 8o away from you. The angle of elevation from you to the top of th

e tree is 20o. Find the slant height of the tree.

Mathematics
1 answer:
Y_Kistochka [10]3 years ago
3 0

Answer:

the height of the tree is <em>15.49 m</em>

<em></em>

Step-by-step explanation:

Step 1:

From the figure, we can determine ∠ATB by using the fact that the sum of all the angles in a triangle add up to 180°:

∠ ATB  = 180° - 98° - 20°

∠ ATB = 62°

Step 2:

Therefore, using the law of sines, we can determine the height of the tree.

TB / sin(20°)  = 40 / sin(62°)

TB = 40 × (sin(20°) / sin(62°))

<em>TB = 15.49 m </em>

<em></em>

Therefore, the height of the tree is <em>15.49 m</em>

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