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mash [69]
2 years ago
5

A man who is 2 meters tall stands on level ground. He is 32 meters from the base of a tree. The angle of elevation of the top of

the tree from his line of sight is 25 degrees. Which equation can be used to solve for the height of the tree? (h = height of the tree)
Mathematics
2 answers:
podryga [215]2 years ago
6 0

Answer:

h = 16.92 m

Step-by-step explanation:

If you mean to man horizontal line of sight  then the height of the tree is:

h = 2m + x

x is one right side and second is distance from the base of a tree 32m.

Tangence in this right triangle is:

tan 25° = x / 32 => x = 32 · tan 25° = 32 · 0.4663 = 14.92m

h = 2 + 14.92 = 16.92m

God with you!!!

valentinak56 [21]2 years ago
5 0

Answer:

H=16.92 (MARK ME AS BRAINIEST)

Step-by-step explanation:

The side opposite 25° is the height of the tree. The side adjacent to 25° is the distance the man is standing from the tree.

tan 25°=  

opposite side

adjacent side

Let h-2 represent the height of the tree

h - 2) = 32 tan 25°

h - 2 = 14.92

h = 16.92 meters

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Answer:

23\sqrt{3}\ un^2

Step-by-step explanation:

Connect points I and K, K and M, M and I.

1. Find the area of triangles IJK, KLM and MNI:

A_{\triangle IJK}=\dfrac{1}{2}\cdot IJ\cdot JK\cdot \sin 120^{\circ}=\dfrac{1}{2}\cdot 2\cdot 3\cdot \dfrac{\sqrt{3}}{2}=\dfrac{3\sqrt{3}}{2}\ un^2\\ \\ \\A_{\triangle KLM}=\dfrac{1}{2}\cdot KL\cdot LM\cdot \sin 120^{\circ}=\dfrac{1}{2}\cdot 8\cdot 2\cdot \dfrac{\sqrt{3}}{2}=4\sqrt{3}\ un^2\\ \\ \\A_{\triangle MNI}=\dfrac{1}{2}\cdot MN\cdot NI\cdot \sin 120^{\circ}=\dfrac{1}{2}\cdot 3\cdot 8\cdot \dfrac{\sqrt{3}}{2}=6\sqrt{3}\ un^2\\ \\ \\

2. Note that

A_{\triangle IJK}=A_{\triangle IAK}=\dfrac{3\sqrt{3}}{2}\ un^2 \\ \\ \\A_{\triangle KLM}=A_{\triangle KAM}=4\sqrt{3}\ un^2 \\ \\ \\A_{\triangle MNI}=A_{\triangle MAI}=6\sqrt{3}\ un^2

3. The area of hexagon IJKLMN is the sum of the area of all triangles:

A_{IJKLMN}=2\cdot \left(\dfrac{3\sqrt{3}}{2}+4\sqrt{3}+6\sqrt{3}\right)=23\sqrt{3}\ un^2

Another way to solve is to find the area of triangle KIM be Heorn's fomula, where all sides KI, KM and IM can be calculated using cosine theorem.

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