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QUESTION
Solve the right triangle.
Round your answers to the nearest tenth.
EXPLANATION
Start

QUESTION $\newline$ Solve the right triangle. $\newline$ Round your answers to the nearest tenth. $\newline$ EXPLANATION $\newline$ Start

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Find probabilities using combinations and permutations

Full solution

Q. QUESTION

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Solve the right triangle.

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Round your answers to the nearest tenth.

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EXPLANATION

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Start

Pythagorean Theorem for Hypotenuse: We need to know at least one side length and one non-right angle, or two side lengths to solve the triangle. Let's assume we know the lengths of the two legs, $a$ and $b$ , and we need to find the hypotenuse $c$ and the angles.
Trigonometric Ratios for Angle A: Use the Pythagorean theorem to find the hypotenuse: $c^2 = a^2 + b^2$ . If $a = 3$ and $b = 4$ , then $c^2 = 3^2 + 4^2 = 9 + 16 = 25$ . So, $c = \sqrt{25} = 5$ .
Inverse Tangent Calculation: Now, let's find the angles. We can use trigonometric ratios. For angle $A$ , opposite side is $a$ and adjacent side is $b$ . So, $\tan(A) = \frac{\text{opposite}}{\text{adjacent}} = \frac{a}{b} = \frac{3}{4}$ .
Angle B Calculation: To find angle $A$ , we take the inverse tangent of $\frac{3}{4}$ . $A = \tan^{-1}\left(\frac{3}{4}\right)$ . Let's say this gives us $A = 36.9$ degrees, rounded to the nearest tenth.
Angle Sum Verification: Since the sum of angles in a triangle is $180$ degrees and one angle is $90$ degrees (right angle), the other angle $B$ can be found by subtracting angle $A$ and the right angle from $180$ . $B = 180 - 90 - A$ . $B = 180 - 90 - 36.9 = 53.1$ degrees.
Angle Sum Verification: Since the sum of angles in a triangle is $180$ degrees and one angle is $90$ degrees (right angle), the other angle $B$ can be found by subtracting angle $A$ and the right angle from $180$ . $B = 180 - 90 - A$ . $B = 180 - 90 - 36.9 = 53.1$ degrees.Check if the angles add up to $180$ degrees. $A + B + 90 = 36.9 + 53.1 + 90 = 180$ degrees. Looks good.

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