It is important to recognize that the bleacher, the ground, and the support form a right triangle with the right angle formed by the intersection of the bleacher wall and the ground. We know the bottom of the support should only be 3ft from the bleacher wall on the ground and the bleacher wall is 10ft high. We will use the Pythagorean Theorem to solve for the length of the support, which is the hypotenuse of this right triangle. Our base of the triangle is 3 feet and the leg is 10 feet.

And so we need a support of 10.44 feet long.

You can draw the following right triangle using the information given by the question:

Since you want to find the height of the platform, you will need to use tangent.

Make sure to round to places after the decimal.

You can draw the following right triangle using the information given by the question:

Since you want to find the height of the platform, you will need to use tangent.

Make sure to round to places after the decimal.

Since and are perpendicular, is a right angle. Since no triangle can have more than one right angle, and is isosceles, must be congruent to . Since angle CBD is congruent to and measures 90 degrees, and can be calculated as follows:

Therefore, and are both equal to 45 degrees. is a 45-45-90 triangle. Therefore, the ratio between side lengths and hypotenuse is . Anyone of the four side lengths of quadrilateral must, therefore, be equal to . To find the area of , multiply two side lengths: .

It is important to recognize that the bleacher, the ground, and the support form a right triangle with the right angle formed by the intersection of the bleacher wall and the ground. We know the bottom of the support should only be 3ft from the bleacher wall on the ground and the bleacher wall is 10ft high. We will use the Pythagorean Theorem to solve for the length of the support, which is the hypotenuse of this right triangle. Our base of the triangle is 3 feet and the leg is 10 feet.

And so we need a support of 10.44 feet long.

Since and are perpendicular, is a right angle. Since no triangle can have more than one right angle, and is isosceles, must be congruent to . Since angle CBD is congruent to and measures 90 degrees, and can be calculated as follows:

Therefore, and are both equal to 45 degrees. is a 45-45-90 triangle. Therefore, the ratio between side lengths and hypotenuse is . Anyone of the four side lengths of quadrilateral must, therefore, be equal to . To find the area of , multiply two side lengths: .

You can draw the following right triangle from the information given by the question.

In order to find the height of the flagpole, you will need to use tangent.

Make sure to round to places after the decimal.

The flagpole is feet tall.

We begin by drawing a picture. Let stand for where the plane reaches a maximum altitude of 31,000 ft. We can also assume that if we draw a line straight down from the plane that it will be perpendicular to the ground. This forms a right triangle.

Now we will use our knowledge of right triangles. We know the trigonometric identity, . We can plug 55 in for our and 31,000 in for the opposite side. Solving for the hypotenuse is solving for the distance from the point of takeoff to the plane when it reaches maximum altitude.

And so the distance from point to the plane at maximum altitude is 37,844 ft.

You can draw the following right triangle from the information given by the question.

In order to find the height of the flagpole, you will need to use tangent.

Make sure to round to places after the decimal.

The flagpole is feet tall.

Since the pictured triangle is a right triangle, the unlabeled angle at the lower left is a right angle measuring 90 degrees. Since interior angles in a triangle sum to 180 degrees, the unlabeled angle at the upper left can be calculated by 180 - 45 - 90 = 45. The pictured triangle is therefore a 45-45-90 triangle. In a 45-45-90 triangle, the two shorter side lengths are equal. Therefore, A = B.