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Find all the missing parts of a right triangle ABC with [tex]C = 90^\circ[/tex], given the following information:

1. [tex]a = 75.8[/tex], [tex]b = 98.3[/tex]

2. [tex]b = 3.3[/tex], [tex]B = 24.5^\circ[/tex]

Answer :

To find the missing parts of a right triangle, we can use trigonometric ratios and the Pythagorean theorem. The missing side lengths a and c can be found using these formulas. The angle A can be found using the inverse tangent function.

To find the missing parts of the right triangle, we can use trigonometric ratios. Given that C is 90◦, we can use the Pythagorean theorem to find the missing side lengths. Let's start by finding side a:

Using the Pythagorean theorem, we can find a:

a² + b² = c²

75.8² + 98.3² = c²

Solving for c, we get: c ≈ 123.8Now, we can find side a using side c:

c² - b² = a²

123.8² - 98.3² = a²

Solving for a, we get: a ≈ 77.4To find angle A, we can use the inverse tangent function:

A = atan(a/b)

A = atan(77.4/98.3)

Solving for A, we get: A ≈ 38.4°

Therefore, the missing parts of the triangle are approximately a = 77.4 and angle A ≈ 38.4°.

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