MATHEMATICS HIGH SCHOOL

Solve the triangle, find m∠A and m∠C. Round angles to the nearest degree.m∠A= __∘

m∠C= __∘
Solve the triangle, find m∠A and m∠C. Round angles to - 1

Answers

Answer 1
Answer:

In the given right triangle ABC, m∠A ≈ 26.44° and m∠C ≈ 63.56°.

To solve the right triangle ABC, we can use trigonometric ratios. In a right triangle, the three main trigonometric ratios are:

1. Sine (sin): \(\sin(\theta) = \frac{{\text{opposite side}}}{{\text{hypotenuse}}}\)

2. Cosine (cos): \(\cos(\theta) = \frac{{\text{adjacent side}}}{{\text{hypotenuse}}}\)

3. Tangent (tan): \(\tan(\theta) = \frac{{\text{opposite side}}}{{\text{adjacent side}}}\)

Given:

AC = 38

AB = 17

To find the angles m∠A and m∠C, we can use the sine and cosine ratios, respectively.

1. For m∠A:

\(\sin(m\angle A) = \frac{{AB}}{{AC}} = \frac{{17}}{{38}}\)\n\n\(m\angle A= \sin^(-1)\left(\frac{{17}}{{38}}\right)\)

2. For m∠C:

\(\cos(m\angle C) = \frac{{AB}}{{AC}} = \frac{{17}}{{38}}\)\n\n\(m\angle C = \cos^(-1)\left(\frac{{17}}{{38}}\right)\)

Let's calculate the angles:

1. \(m\angle A \approx \sin^(-1)\left(\frac{{17}}{{38}}\right) \approx 26.44^\circ\)\n\n2. \(m\angle C \approx \cos^(-1)\left(\frac{{17}}{{38}}\right) \approx 63.56^\circ\)

Therefore, m∠A ≈ 26.44° and m∠C ≈ 63.56° (rounded to the nearest degree).

To know more about right triangle, refer here:

brainly.com/question/31613708

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Answer 2
Answer:

Answer:

m\angle A=63^\circ\nm\angle C=26^\circ

Step-by-step explanation:

Trigonometric Ratios

The ratios of the sides of a right triangle are called trigonometric ratios. The longest side of the triangle is called the hypotenuse and the other two sides are called the legs.

Selecting any of the acute angles as a reference, it has an adjacent side and an opposite side. The trigonometric ratios are defined upon those sides.

The cosine ratio is defined as:

\displaystyle \cos\theta=\frac{\text{adjacent leg}}{\text{hypotenuse}}

Note the angle A of the figure has 17 as the adjacent leg and 38 as the hypotenuse, so we can directly apply the formula:

\displaystyle \cos A=(17)/(38)

\cos A=0.4474

Using a scientific calculator, we get the inverse cosine:

A=\arccos(0.4474)

A\approx 63^\circ

Since A+B+C=180°, we can solve for C:

C = 180° - A - B

C = 180° - 63° - 90°

C = 26°

Thus:

m\angle A=63^\circ\nm\angle C=26^\circ

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Answers

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Answers

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