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3 years ago

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solve a right triangles with an acute angle of 14° and hypotenuse length of 100m. Express the angle to the nearest degree and th

e lengths to the nearest tenth of a metre.

1 answer:

Romashka-Z-Leto [24]3 years ago

3 0

I’m having a hard time understanding your question

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Please help me out :P

Veseljchak [2.6K]

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

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5 0

2 years ago

HELP NOW PLS I BEG OF U The side lengths of a right triangle are 10, 24, and 26. Determine which is the length of the hypotenuse

gregori [183]

Answer:

hypotenuse length is 26

Step-by-step explanation:

a²+b²=c²

10²+24²=c²

100+576=c²

√676=26

5 0

3 years ago

Can someone help me plz??

Brrunno [24]

Answer: 23

Step-by-step explanation:

2x + 14 = 60

2x = 46

x = 23

6 0

3 years ago

Amber needs to select six players for her volleyball team. there are 10 players to choose from. how many possible combinations o

Dima020 [189]

Amber can make a possible number of 12 different teams

8 0

3 years ago

0=(x+3)(x-2)?????????

VLD [36.1K]

Answer:

x=-3, x=2 or x=3,2

4 0

4 years ago