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2 years ago

Find the measures of the interior angles of the triangle.

Mathematics

2 answers:

OlgaM077 [116]2 years ago

4 0

Answer:

∠ A = 140° , ∠ B = 30° , ∠ C = 10°

Step-by-step explanation:

the sum of the 3 interior angles = 180°

sum the given angles and equate to 180

x - 5 + 2x + 140 = 180

3x + 135 = 180 ( subtract 135 from both sides )

3x = 45 ( divide both sides by 3 )

x = 15

then

∠ A = 140°

∠ B = 2x = 2 × 15 = 30°

∠ C = x - 5 = 15 - 5 = 10°

frutty [35]2 years ago

4 0

Answer:

<h2>Angle A = 140°</h2><h2>Angle B = 30°</h2><h2>Angle C = 10°</h2>

Step-by-step explanation:

Find the measures of the interior angles of the triangle.

The sum of the interior angles of a triangle is 180°

180 = 140 + 2x + x - 5

40 + 5 = 3x

45 = 3x

x = 45 : 3

x = 15°

-----------------------

check

180 = 140 + 2 * 15 + 15 - 5

180 = 180

the answer is good

---------------------------

Find the angles

140° = angle A

2x = 15 * 2

2x = 30° (angle B)

x - 5 = 15 - 5

x = 10° ( angle C)

-----------------------

check

140 + 30 + 10 = 180°

the answer is good

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Help with length of hypotenuse

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Answer:

sqrt(10) *x

Step-by-step explanation:

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3 years ago

Read 2 more answers

Fred the owl is looking down at a 67° angle from the top of a tree that is 15 ft tall, when he spots a bird on the ground. How f

guapka [62]

Answer:

Fred C. 16.30 ft

Gary B. 169.67 m

Step-by-step explanation:

Fred the owl...

Always draw a diagram first (see diagram below). We assume trees are perpendicular (at 90°) to the ground. The situation forms a right-angle triangle.

We need to find "x", which is the direct distance between the owl and the bird. "x" is also the hypotenuse, which is the longest side in a right-angle triangle. Since we know a side and an angle, we can find the hypotenuse using primary trigonometry ratios.

∠B will be the angle of reference (the angle we are "talking" about). The side we know is opposite to ∠B (15ft). We know it's opposite because it's not touching the angle. The side we need to find is the hypotenuse.

Use the trig. ratio sine because it has opposite and hypotenuse in it. The general formula is:

sinθ = opp/hyp

θ means the angle, and we know it is 67°.

Replace all the information you know:

sinB = opp/hyp

sin67° = (15ft) / x Isolate "x". Rearrange the equation.

xsin67° = (15ft) Divide both sides by sin67°

x = (15ft) / sin67°

x = 16.295... ft Exact answer in decimals

x ≈ 16.30 ft Rounded to nearest hundredth

Therefore Fred the owl is 16.30 feet from the bird.

Gary spots a monkey...

Draw a diagram first (see below). G is Gary, M is the monkey, T is the bottom of the Sears Tower. We need to find "x", which is the distance between the monkey and the bottom of the tower.

The angle of reference is M, which is 69°. We need to find the adjacent side and we know the opposite side. The trig. ratio that has adjacent and opposite is tangent.

tanθ = opp/adj

Replace all the information you know:

tanM = opp/adj

tan69° = (442m) / x Rearrange the formula to isolate "x"

xtan69° = 442m Divide both sides by tan69°

x = 442m / tan69° Solve by dividing

x = 169.6679.... m Exact decimal answer

x ≈ 169.67m Rounded to the nearest hundredth

Therefore the monkey is 169.67 metres from the tower.

Remember all the trig. ratios using the acronym SohCahToa.

o = opposite side

a = adjacent side

h = hypotenuse side

S = sine, sin for short

C = cosine, cos for short

T = tangent, tan for short

The operation is always dividing the first side in the acronym by the second side.

sinθ = opp/hyp

cosθ = adj/hyp

tanθ = opp/adj

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