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Whitepunk [10]
2 years ago
10

What is the value of x?

Mathematics
2 answers:
djverab [1.8K]2 years ago
6 0

Answer:

x = 55°

Step-by-step explanation:

Hello!

The sum of angles in a triangle is 180°.

To solve for x, we have to subtract the given angles from 180°.

<h3>Solve for x</h3>
  • 180° = ∠1 + ∠2 + ∠x
  • 180° = 75° + 50° + x°
  • 180° - 75° - 50° = x°
  • 55° = x°

The value of x is 55°.

Ronch [10]2 years ago
4 0

<u>Angle sum property of a triangle</u>

  • Angle sum property of triangle states that the sum of interior angles of a triangle is 180°.

∠A + ∠B + ∠C = 180°

  • ∠A = ?
  • ∠B = 75°
  • ∠C = 50°

We need to find the value of ∠A

According to the angle sum property of a triangle

⇢∠A + ∠B + ∠C = 180°

⇢∠A + 75° + 50° = 180°

⇢∠A + 125° = 180°

⇢∠A = 180° - 125°

⇢∠A = 55°

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Problem 9, part a)

Compass bearings always have north as the starting point. This is where 0 degrees is situated, and 360 degrees as well. As the bearing angle increases, you'll turn to the right toward the eastward direction. Effectively you're sweeping out a clockwise rotation. The bearing 322 degrees is in a northwest position as the diagram shows (place the ship at the bottom right corner of the triangle). The bottom right acute angle of the triangle is 322 - 270 = 52 degrees. This is the reference angle we'll use for finding the distance d.

With respect to the reference angle of 52 degrees, the side 18.5 is the opposite side and d is the adjacent side. Use the tangent ratio to get...

tan(angle) = opposite/adjacent

tan(52) = 18.5/d

d*tan(52) = 18.5

d = 18.5/tan(52)

d = 14.4537840903742

The approximate value of d is 14.4537840903742 km

This rounds to 14.5 when rounding to one decimal place.

<h3>Answer: 14.5 km</h3>

=======================================================

Problem 9, part b)

Recall that

distance = rate*time

where "rate" is another term for "speed" or "velocity"

We can solve this for the time to get

time = distance/rate

------

We found the distance back in part a) above. We are given the rate of 48 km/h

So,

time = distance/rate

time = 14.4537840903742/48

time = 0.3011205018828

This is the time it takes in hours. Multiply by 60 to convert to minutes

0.3011205018828 hours = 60*0.3011205018828 = 18.067230112968 minutes

This rounds to the whole number 18

<h3>Answer: 18 minutes</h3>
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