QQuestionMathematics
QuestionMathematics
Find the length of the missing side of the triangle. Round to the nearest tenth (first decimal place).
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Answer
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Step 1:
\sin(\theta) = \frac{opposite}{hypotenuse}
First, we need to identify the given side lengths and the missing side. In a right triangle, the relationship between the side lengths and the angles is given by the trigonometric functions sine, cosine, and tangent. We can use the sine function to find the length of the missing side. The sine of an angle in a right triangle is defined as the ratio of the length of the opposite side to the length of the hypotenuse.
Step 2:
opposite = hypotenuse \times \sin(\theta)
In our triangle, the opposite side is the missing side, and the hypotenuse is the side with length 7 units. We can rearrange the sine function to solve for the length of the opposite side:
Step 3:
opposite = 7 \times \sin(\theta)
Substituting the given values into the equation, we get:
Step 4:
\sin(36.87^\circ) \approx 0.6
From the given triangle, we can see that $\theta$ is an acute angle, and its measure is approximately 36.87 degrees. We can use a calculator to find the sine of this angle:
Step 5:
opposite = 7 \times 0.6 \approx 4.2
Substituting this value into the equation, we get:
Step 6:
Therefore, the length of the missing side is approximately 4.2 units.
Final Answer
The length of the missing side is approximately 4.2 units.
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