# Aright triangle has side lengths ac = 7 inches, bc = 24 inches, and ab = 25 inches. what are the measures of the angles

###### Question:

what are the measures of the angles in triangle abc?

(a.) m∠a ≈ 46.2°, m∠b ≈ 43.8°, m∠c ≈ 90°

(b.) m∠a ≈ 73.0°, m∠b ≈ 17.0°, m∠c ≈ 90°

(c.) m∠a ≈ 73.7°, m∠b ≈ 16.3°, m∠c ≈ 90°

(d.) m∠a ≈ 74.4°, m∠b ≈ 15.6°, m∠c ≈ 90°

plz every time i try to do the problem my answer doesnt show up but i have no idea what im doing

its not d tho, i know that much

## Answers

⁻⁻Using Sine ratio: opposite / Hypotenuse

Opposite to angle A = 24, Hypotenuse = 25

Sin A = 24 / 25

Sin A = 0.96

A = Sin⁻¹(0.96) Use a calculator.

A ≈73.74°

A ≈ 73.7°

∠A + ∠B = 90° Since it is a right angled triangle.

∠B = 90° - ∠A

∠B = 90° - 73.7°

∠B = 16.3°

(c.) m∠A ≈ 73.7°, m∠B ≈ 16.3°, m∠C = 90°

c.) m∠A ≈ 73.7°, m∠B ≈ 16.3°, m∠C ≈ 90°

Step-by-step explanation:

A right triangle has side lengths AC = 7 inches, BC = 24 inches, and AB = 25 inches.

What are the measures of the angles in triangle ABC?

a.) m∠A ≈ 46.2°, m∠B ≈ 43.8°, m∠C ≈ 90°

b.) m∠A ≈ 73.0°, m∠B ≈ 17.0°, m∠C ≈ 90°

c.) m∠A ≈ 73.7°, m∠B ≈ 16.3°, m∠C ≈ 90°

d.) m∠A ≈ 74.4°, m∠B ≈ 15.6°, m∠C ≈ 90°

(C)

Step-by-step explanation:

It is given that a right triangle, ACB which is right angled at C has BC = 24 inches, and AB = 25 inches.

We know that m∠C=90°,

Using the trigonometry in ΔACB, we have

[tex]sinB=\frac{AC}{AB}[/tex]

Substituting the given values, we get

⇒[tex]sinB=\frac{24}{25}[/tex]

⇒[tex]B=sin^{-1}(0.96)[/tex]

⇒[tex]B=73.7^{\circ}[/tex]

Also, [tex]sinA=\frac{CB}{AB}[/tex]

Substituting the given values, we get

⇒[tex]sinA=\frac{7}{25}[/tex]

⇒[tex]A=sin^{-1}(0.28)[/tex]

⇒[tex]A=16.3^{\circ}[/tex]

Therefore, the measure of the angles in triangle ABC are m∠A ≈ 73.7°, m∠B ≈ 16.3°, m∠C ≈ 90°.

Thus, option C is correct.

[tex]Aright triangle has side lengths ac = 7 inches, bc = 24 inches, and ab = 25 inches. what are the mea[/tex]

90, 74, 16 degrees

Step-by-step explanation:

Given that a right triangle has side lengths AC = 7 inches, BC = 24 inches, and AB = 25 inches.

We find that

AC square + BC square = AC square

[tex]7^2 +24^2 =625 = 25^2[/tex]

So angle C = 90 degrees.

sin A = 24/25

So A = 74 degrees and B = 16 degrees

C) m∠A ≈ 73.7°, m∠B ≈ 16.3°, m∠C ≈ 90°

C

Step-by-step explanation:

correct on edg2020

m∠C ≈ 90°m∠A ≈ 73.7°, m∠B ≈ 16.3°

Step-by-step explanation:

Given:

triangle ABC is right-angled triangle

let angle C= 90

using law of sines:

a/sinA=b/sinB

Putting the values:

25/sin90= 7/sinB

25/1=7/sinB

25sinB=7

sinB=7/25

sinB=0.28

B=sin^-1 (0.28)

B=16.3

As C= 90, B=16.3

A= 180-(90+16.3)

A=180-(106.3)

A=73.7 !

Angle C is 90 degrees

Angle B is 16

Angle A is 74

m∠A =73.7°

m∠B = 16.3°

m∠C = 90°

The measures should be

M∠A≈73.7°,M∠B≈≈16.3°,M∠C=90°