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cestrela7 [59]
3 years ago
7

Jason places a mirror on the ground 40 feet from the base of a tree. He walks backwards until he can see the top of the tree in

the middle of the mirror. At that point, Jason's eyes are 6 feet above the ground and he is 8 feet from the image in the mirror. What is the height of the tree?
Mathematics
2 answers:
Bas_tet [7]3 years ago
7 0
Let
x---------------> <span>the height of the tree

we know that
by using proportion
</span>\frac{40}{8} = \frac{x}{6}  \\  \\ 40*6=8*x \\  \\ x=40*6/8 \\  \\ x=30 feet
<span>
therefore

the answer is
</span><span>the height of the tree is </span>30feet
maksim [4K]3 years ago
3 0
We have to use a proportion:x is the height of a treex : 40 = 6 : 88 x = 6 * 408 x = 240x = 240 : 8x = 30 ftAnswer:The height of the tree is 30 ft.

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cos θ = \frac{-4\sqrt{65} }{65}, sin θ = \frac{-7\sqrt{65} }{65}, cot  θ  = 4/7, sec  θ = \frac{-\sqrt{65} }{4}, cosec  θ  = \frac{-\sqrt{65} }{7}

<h3>What are trigonometric ratios?</h3>

Trigonometric Ratios are values of all the trigonometric functions based on the value of the ratio of sides in a right-angled triangle.

Sin θ: Opposite Side to θ/Hypotenuse

Tan θ: Opposite Side/Adjacent Side & Sin θ/Cos

Cos θ: Adjacent Side to θ/Hypotenuse

Sec θ: Hypotenuse/Adjacent Side & 1/cos θ

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tan θ = opposite/adjacent = 7/4

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we now look for the hypotenuse of the right angled triangle

hypotenuse = \sqrt{7^{2} + 4^{2} } = \sqrt{49+16} = \sqrt{65}

sin θ = opposite/ hyp = \frac{7}{\sqrt{65} }

Rationalize, \frac{7}{\sqrt{65} } x \frac{\sqrt{65} }{\sqrt{65} } = \frac{7\sqrt{65} }{65}

But θ is in the third quadrant(180 - 270) and in the third quadrant only tan and cot are positive others are negative.

Therefore, sin θ = - \frac{7\sqrt{65} }{65}

cos   θ  = adj/hyp = \frac{4}{\sqrt{65} }

By rationalizing and knowing that cos  θ  is negative, cos θ  = -\frac{-4\sqrt{65} }{65}

cot θ  = 1/tan θ  = 1/7/4 = 4/7

sec θ  = 1/cos θ  = 1/\frac{4}{\sqrt{65} } = -\frac{-\sqrt{65} }{4}

cosec θ  = 1/sin θ  = 1/\frac{\sqrt{65} }{7} = \frac{-\sqrt{65} }{7}

Learn more about trigonometric ratios: brainly.com/question/24349828

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