Question

A tree is broken due to the storm in such a way that the top of the tree touches the ground and makes an angle of 300 with the ground. Length of the broken upper part of the tree is 8 meters. Find the height of the tree before it was broken.​

Answer 1

we know that the broken part of the tree becomes the hypotenuse and makes 300 with the ground

so the perpendicular will be the unbroken part of the tree.

(please draw the diagram to understand according to what said before)

so we know sinФ=perpendicular/hypotenuse

so sin30=unbroken part of the tree/broken part of the tree(hope u understand that the broken part has become the hypotenuse)

so sin30=unbroken part/8

1/2=unbroken part/8

so unbroken part=8×1/2=4m

so the height of the tree before it was broken=unbroken part+broken part=4+8=12m

ans:=12m

hope this helps you

thanks

Answer 2

Answer: the height of the tree before it was broken is approximately 8.944 meters.

Step-by-step explanation:

We can use the trigonometry to solve the problem. Let h be the height of the tree before it was broken, and x be the distance between the base of the tree and the point where the top of the tree touches the ground.

We know that:

sin 300 = x/h

8 = x/sin 300

x = 8sin 300

Since sine of 300 is 1/2, x=8*1/2 = 4

To find the height of the tree before it was broken, we can use the Pythagorean theorem:

h^2 = x^2 + (8)^2

h^2 = 4^2 + 8^2

h = sqrt(16 + 64)

h = sqrt(80)

h = 8.944

So the height of the tree before it was broken is approximately 8.944 meters.

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