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vitfil [10]
3 years ago
10

Melissa sees a lighthouse from her sailboat. She knows the height of the lighthouse is 154 feet. She uses a measuring device and

determines that the angle to the top of the lighthouse from her boat is 35°. How far is the sailboat from the base of the lighthouse?

Mathematics
2 answers:
Alex_Xolod [135]3 years ago
6 0

Answer:

219.9  feet to the nearest tenth.

Step-by-step explanation:

Use trigonometry:

tan 35 = opposite / adjacent side

= 154/x

x =  154 / tan35

= 219.93

julsineya [31]3 years ago
6 0

Answer:

219.9 ft

Step-by-step explanation:

After looking at pic, cross multiply to get x tan(35)=154

then divide both sides by tan(35) giving x=154/tan(35)

x is approximately 219.9 ft

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3 years ago
Tyrone went to a basketball game and bought a jersey that was on sale at a 30% discount. He also bought a hat that cost $37.89.
Dmitry [639]

Answer:

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Step-by-step explanation:

<u>First, we need to determine how much he spent on the jersey:</u>

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7 0
3 years ago
Solve sin x - (3sin x-1) = 0
soldi70 [24.7K]

Answer:

\large\boxed{x=\dfrac{\pi}{6}+2k\pi\ \vee\ x=\dfrac{5\pi}{6}+2k\pi,\ k\in\mathbb{Z}}

Step-by-step explanation:

\sin x-(3\sin x-1)=0\\\\\sin x-3\sin x+1=0\qquad\text{subtract 1 from both sides}\\\\-2\sin x=-1\qquad\text{divide both sides by 2}\\\\\sin x=\dfrac{1}{2}\Rightarrow x=\dfrac{\pi}{6}+2k\pi\ \vee\ x=\dfrac{5\pi}{6}+2k\pi,\ k\in\mathbb{Z}

\text{Equation:}\\\\\sin x=a\\\\\text{has solutions}\\\\x=\theta+2k\pi\ \vee\ x=(\pi-\theta)+2k\pi\\\\\text{Why}\ 2k\pi?\\\text{Because the sine function has a period of}\ 2\pi.

\text{look at the table}\\\\\sin x=\dfrac{1}{2}\to x=\dfrac{\pi}{6}\ \vee\ x=\pi-\dfrac{\pi}{6}=\dfrac{5\pi}{6}

\text{Other solution:}\\\\\sin x=\dfrac{1}{2}\Rightarrow x=\sin^{-1}\dfrac{1}{2}\\\\x=\dfrac{\pi}{6}+2k\pi\ \vee\ x=\dfrac{5\pi}{6}+2k\pi

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