A right triangle has sides of 6cm,8cm, and 10cm. Determine the measure of the smallest angle, theta.

Identify Shortest Side: To find the smallest angle in a right triangle, we can use the trigonometric functions. The smallest angle will be opposite the shortest side. In this case, the shortest side is 6cm. We can use the cosine function since we know the lengths of the adjacent side (8cm) and the hypotenuse (10cm). Cos(theta) = adjacent side / hypotenuse Cos(theta) = 8cm / 10cmCalculate Cosine Value: Now we calculate the value of Cos(theta). Cos(theta) = 8 / 10 Cos(theta) = 0.8Find Angle using Inverse Cosine: Next, we need to find the angle whose cosine is 0.8. We can do this by using the inverse cosine function, also known as arccos. theta = arccos(0.8)Calculate Theta: Using a calculator, we find the measure of theta. theta ≈ arccos(0.8) ≈ 36.87 degrees

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A right triangle has sides of
6cm,8cm, and
10cm. Determine the measure of the smallest angle,
theta.

A right triangle has sides of $6 \mathrm{~cm}, 8 \mathrm{~cm}$ , and $10 \mathrm{~cm}$ . Determine the measure of the smallest angle, $\theta$ .

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Math Problems

Grade 6

Find missing angles in special triangles

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Q. A right triangle has sides of

6 \mathrm{~cm}, 8 \mathrm{~cm}

, and

10 \mathrm{~cm}

. Determine the measure of the smallest angle,

\theta

Identify Shortest Side: To find the smallest angle in a right triangle, we can use the trigonometric functions. The smallest angle will be opposite the shortest side. In this case, the shortest side is $6\,\text{cm}$ . We can use the cosine function since we know the lengths of the adjacent side ( $8\,\text{cm}$ ) and the hypotenuse ( $10\,\text{cm}$ ). $\newline$ $\cos(\theta) = \frac{\text{adjacent side}}{\text{hypotenuse}}$ $\newline$ $\cos(\theta) = \frac{8\,\text{cm}}{10\,\text{cm}}$
Calculate Cosine Value: Now we calculate the value of $\text{Cos}(\theta)$ . $\text{Cos}(\theta) = \frac{8}{10}$ $\text{Cos}(\theta) = 0.8$
Find Angle using Inverse Cosine: Next, we need to find the angle whose cosine is $0.8$ . We can do this by using the inverse cosine function, also known as arccos. $\newline$ $\theta = \arccos(0.8)$
Calculate Theta: Using a calculator, we find the measure of theta. $\theta \approx \arccos(0.8) \approx 36.87$ degrees