Mike wants to work out the height of a tree with a fence all around it. from a he can see the angle of elevation is 19°

The height of the tree is 13.8m and this can be determined by using the trigonometric function and sine law.

Given :

The following calculation can be used to determine the height of a tree.

In triangle ATB the exterior angle at B =

Applying sine law:

Now, the value of sin32 is:

Height = 13.8m

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The height of tree ≈ 13.8 m.

Step-by-step explanation:

The rest of the question is as shown in the attached figure.

As shown:

In ΔABT :Exterior angle at B = ∠A + ∠ATB

∠ATB = 32° - 19° = 13°

Using the sine law:

In ΔOBT :

Sin 32 = opposite/hypotenuse = h/BT

h = BT * sin 32

Substitute with the value of BT

h = 18 * sin 19* sin 32 / sin 13= 13.8 m

So, The height of tree ≈ 13.8 m.

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