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monitta
3 years ago
7

I need help with these two questions!! I got 72° for Question 7, I don't know I need help with both of them!! PLEASE HELP!! :)

Mathematics
1 answer:
Nat2105 [25]3 years ago
3 0

Answer:

7. 49

8. 10.4

Step-by-step explanation:

7) our hypotenuse is 8, and the side opposite the base of ladder and ground angle is 6, therefore we can use Sin

sin = opposite/hypotenuse

sin(x) = 6/8 = 3/4

sin-1(3/4) = 49

8) using the theorem that alternate exterior angles are congruent

the angle opposite side x is 30

tan = opposite/adjacent

tan(30) = x/18

x = 18tan(30) = 6√(3) = 10.4

you can also use 30-60-90 special right triangles.

the side opposite 30 is x

side opposite 60 is x√(3)

and side opposite 90 is 2x

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Please help me out :P
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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

Analysis:

tan θ = opposite/adjacent = 7/4

opposite = 7, adjacent = 4.

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

#SPJ1

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