A right triangle has a hypotenuse of length 40 and an angle of 25°, with a side opposite this angle of length 16. A second right triangle also has an angle of 25°, with a hypotenuse of length 10. Determine the length of the side opposite the 25° angle on the second triangle.(1 point)

Question

Responses

The side opposite the second triangle’s 25° angle has length 64.
The side opposite the second triangle’s 25° angle has length 64.

The side opposite the second triangle’s 25°angle has length 821−−√
.
The side opposite the second triangle’s 25°angle has length 8 Start Root 21 End Root .

The side opposite the second triangle’s 25° angle has length 4.
The side opposite the second triangle’s 25° angle has length 4.

The side opposite the second triangle’s 25° angle has length 8.

Answer 1

To find the length of the side opposite the 25° angle in the second triangle, we can use the sine function, which relates the angle to the lengths of the sides in a right triangle.

The formula we will use is:

\[ \text{Opposite} = \text{Hypotenuse} \times \sin(\text{Angle}) \]

From the problem, we know:

• The hypotenuse of the second triangle is 10.
• The angle is 25°.

Now we can calculate the opposite side using the sine of 25°:

\[ \text{Opposite} = 10 \times \sin(25°) \]

Using a calculator to find \(\sin(25°)\):

\[ \sin(25°) \approx 0.4226 \]

Now we substitute this value into the equation:

\[ \text{Opposite} \approx 10 \times 0.4226 \approx 4.226 \]

Therefore, rounding to the nearest integer, the length of the side opposite the 25° angle in the second triangle is approximately 4.

Thus, the side opposite the second triangle’s 25° angle has length 4.