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ivolga24 [154]
2 years ago
9

A boat captain can see a lighthouse on the shore which is 103ft in front of him. If the lighthouse is 22ft tall, at what angle o

f elevation can the captain see the top of the lighthouse? options: 45° 12° 77° 11°
Mathematics
1 answer:
elena-14-01-66 [18.8K]2 years ago
5 0

Answer:

  • 21°

Step-by-step explanation:

A boat captain, lighthouse and its base form a right triangle.

<u>We need to find the angle opposite to 22 ft side:</u>

  • tan x = 22/103
  • x = arctan (22/103)
  • x = 21°

<em>Note, option D should read 21° not 11°</em>

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So,

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Can someone help me with this thanks ​
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The length of the brace required is 4.3m

What is sine rule?

In a ΔABC a, b and c are the sides and A, B and C are angles then,

\frac{a}{SinA}=\frac{b}{sinB}=\frac{c}{sinC}

We can find the length, l as shown below:

Let AB=3m, BC=2m and AC=l

Let ∠A=25°

So, in ΔABC

\frac{BC}{sinA}=\frac{AB}{sinC}=\frac{AC}{SinB}

\frac{BC}{sinA}=\frac{AB}{sinC}

\frac{2}{sin25}=\frac{3}{sinC}

\angle{C}=sin^{-1}(\frac{3\times sin25}{2} )

∠C=39.34°

∠A+∠B+∠C=180°

∠B=180°-25°-39.34°

∠B=115.66°

\frac{BC}{sinA}=\frac{AC}{SinB}

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l=\frac{2\times sin(115.66)}{sin25}

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Rounding to nearest tenth of meter.

l=4.3m

Hence, the length of the brace required is 4.3m

Learn more about Sine Rule here:

brainly.com/question/25852087

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