Question

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°

Answer 1

Answer:

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:

$\frac{AB}{sinT} =\frac{BT}{sinA} \\BT = \frac{AB}{SinT} *sinA = \frac{18}{sin13} *sin19$

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.

Answer 2

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

Given :

• From A Mike can see the angle of elevation is 19°.
• From B, 18m closer, the angle of elevation is $32^\circ$.

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

In triangle ATB the exterior angle at B = $\rm \angle A + \angle ATB$

$\rm \angle ATB = 32^\circ-19^\circ=13^\circ$

Applying sine law:

$\rm \dfrac{AB}{sin T}=\dfrac{BT}{sin A}$

$\rm BT = \dfrac{sin A }{sin T}\times AB$

$\rm BT = \dfrac{sin19}{sin13}\times 18$

Now, the value of sin32 is:

$\rm sin32 = \dfrac{Height}{BT}$

$\rm \dfrac{sin 32 \times sin 19\times 18}{sin13} = h$

Height = 13.8m

For more information, refer to the link given below:

https://brainly.com/question/17289163