1. What is the value of x in the right triangle below? If needed, round your answer to two decimal places.

32 angle, 15 inches, find the x in base…

2. A 10-foot ladder is leaning up against the side of a building so that the top of the ladder reaches the top of the building. If the ladder meets the building at a 32 angle, then what is the height of the building? If needed, round your answer to two decimal places. 10 feet

3. What is the value of in the right triangle below? If needed, round your answer to two decimal places. 2 ft and the other is 5 ft

4. What is the length of the altitude in the isosceles right triangle below? If needed, round your answer to two decimal places. 41 angle, 41 angle, 10 mm

5. A plane is flying at an altitude of 6,304 feet above the ground. From a point that is 10,000 feet from the plane, what is the angle of elevation to the plane? If needed, round your answer to two decimal places.

the answer is 10

done.

i neeed this done in 20 minutes, please help!!!!!!!!!!!!!

1. To find the value of x in the right triangle, we can use the trigonometric function tangent. Tangent is defined as the ratio of the length of the opposite side to the length of the adjacent side. In this case, the opposite side to angle 32 degrees is x, and the adjacent side is 15 inches. So we have:

tan(32°) = x / 15

To solve for x, we can rearrange the equation:

x = 15 * tan(32°)

Using a calculator or trigonometric table, find the tangent of 32 degrees, and then multiply it by 15.

2. To find the height of the building in this scenario, we can use the trigonometric function sine. Sine is defined as the ratio of the length of the opposite side to the length of the hypotenuse. In this case, the ladder is the hypotenuse, and its length is 10 feet. The opposite side to the angle of 32 degrees is the height of the building we want to find. So we have:

sin(32°) = height / 10

To solve for the height, we can rearrange the equation:

height = 10 * sin(32°)

Using a calculator or trigonometric table, find the sine of 32 degrees, and then multiply it by 10.

3. In this right triangle, we can use the Pythagorean theorem to find the value of the missing side. The Pythagorean theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. In this case, we have one side measuring 2 ft and the other measuring 5 ft. Let's call the missing side x. So we have:

x^2 = 2^2 + 5^2

To solve for x, we can simplify the equation and take the square root of both sides:

x^2 = 4 + 25
x^2 = 29
x = √29

Calculate the square root of 29 to get the value of x.

4. In an isosceles right triangle, the two acute angles are equal (in this case, 41 degrees), and the ratio between the length of the hypotenuse and the length of each leg is √2. So if one leg measures 10 mm, the length of the hypotenuse is:

hypotenuse = leg * √2

hypotenuse = 10 * √2

To find the length of the altitude (the segment perpendicular to the hypotenuse), we can use the trigonometric function sine. Sine is defined as the ratio of the length of the opposite side to the length of the hypotenuse. In this case, the opposite side to the 41 degrees angle is the altitude we want to find, and the hypotenuse is 10 * √2. So we have:

sin(41°) = altitude / (10 * √2)

To solve for the altitude, we can rearrange the equation:

altitude = (10 * √2) * sin(41°)

Using a calculator or trigonometric table, find the sine of 41 degrees, and then multiply it by 10 * √2.

5. To find the angle of elevation to the plane, we can use the trigonometric function arctan (inverse tangent). Arctan is the inverse of tangent and allows us to find an angle given the ratio of the lengths of the sides. In this case, the altitude of the plane is 6,304 feet, and the distance from the plane is 10,000 feet. The angle of elevation is the angle between the line of sight from the ground to the plane and the horizontal. So we have:

angle of elevation = arctan(altitude / distance)

angle of elevation = arctan(6,304 / 10,000)

Using a calculator or trigonometric table, find the arctangent of the ratio 6,304/10,000 to get the angle of elevation.

This certainly looks like a test to me. Sorry.