Solve the right triangle shown in the figure. A=55.8^(@),c=51 a. What are the lengths of the sides? a≈◻ (Round to the nearest hundredth as needed.)

Use Cosine Function: To find the length of side a, we can use the cosine function since we have the angle A and the hypotenuse c. The cosine of an angle in a right triangle is equal to the adjacent side (which is a in this case) divided by the hypotenuse (which is c). The formula is: cos(A) = a/c We can rearrange this formula to solve for a: a = c * cos(A) Now we can plug in the values we know: A = 55.8 degrees c = 51 a = 51 * cos(55.8°) First, we need to calculate the cosine of 55.8 degrees.Calculate Cosine of Angle: Using a calculator, we find: cos(55.8°) ≈ 0.5623 Now we can multiply this by the length of side c to find side a: a = 51 * 0.5623Find Length of Side a: Performing the multiplication gives us: a ≈ 28.6773 We are asked to round to the nearest hundredth, so: a ≈ 28.68

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Solve the right triangle shown in the figure. $\newline$ $A=55.8^\circ$ , $c=51$ $\newline$ $a\approx$ ◻ (Round to the nearest hundredth as needed.)

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Q. Solve the right triangle shown in the figure.

\newline

A=55.8^\circ

c=51

\newline

a\approx

◻ (Round to the nearest hundredth as needed.)

Use Cosine Function: To find the length of side $a$ , we can use the cosine function since we have the angle $A$ and the hypotenuse $c$ . The cosine of an angle in a right triangle is equal to the adjacent side (which is $a$ in this case) divided by the hypotenuse (which is $c$ ). The formula is: $\newline$ $\cos(A) = \frac{a}{c}$ $\newline$ We can rearrange this formula to solve for $a$ : $\newline$ $a = c \cdot \cos(A)$ $\newline$ Now we can plug in the values we know: $\newline$ $A = 55.8$ degrees $\newline$ $c = 51$ $\newline$ $a = 51 \cdot \cos(55.8^\circ)$ $\newline$ First, we need to calculate the cosine of $55.8$ degrees.
Calculate Cosine of Angle: Using a calculator, we find: $\newline$ $\cos(55.8^\circ) \approx 0.5623$ $\newline$ Now we can multiply this by the length of side $c$ to find side $a$ : $\newline$ $a = 51 \times 0.5623$
Find Length of Side $a$ : Performing the multiplication gives us: $\newline$ $a \approx 28.6773$ $\newline$ We are asked to round to the nearest hundredth, so: $\newline$ $a \approx 28.68$