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

For more information, refer to the link given below:

link

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.

- "runner b is moving at a slower rate."

- "the graphs shown are graphs of distance(km) against time(min).

the slopes of this graphs are are given by:

slope = (change in y)/(change in x)

= (change in distance)/(change in time)

this is the formula for finding the speed. so, the slope of these graphs represent the speed of the runner.

taking each division in the graph to represent 1 on both axis:

runner a ⇒ speed = (2-0)/(1-0)

= 2/1

= 2 km/min

runner b ⇒ speed = (3-0)/(3-0)

= 3/3

= 1 km/min

this shows that   runner b is moving at a slower rate."