Question

В четырехугольнике АВСД угол А=90 градусов, уголДВС-90градусов. найти АВ?

Answer 1

Сначала по теореме Пифагора находишь ВС  ВС^2 = 34^2 - 16^2 BC^2 = 900 BC = 30  А теперь по той же теореме Пифагора находишь АВ  АB^2 = BC^2 = 24^2 AB^2 = 900 - 576 AB^2 = 324 AB = 18

Answer 2

Finding the length of AB in quadrilateral ABCD

To find the length of AB in quadrilateral ABCD, we need to use the given information about the angles in the quadrilateral. According to the information provided, angle A is 90 degrees and angle DVS is -90 degrees.

To solve this problem, we can use the properties of a quadrilateral and trigonometry. Let's break down the steps to find the length of AB:

1. Use the fact that the sum of the angles in a quadrilateral is 360 degrees. Since angle A is 90 degrees and angle DVS is -90 degrees, the sum of the other two angles (angle B and angle C) must be 360 - 90 - (-90) = 360 degrees.

2. Apply trigonometry to find the length of AB. We can use the cosine rule or the sine rule, depending on the given information. Since we have the length of AD and the measure of angle A, we can use the cosine rule.

The cosine rule states that in a triangle with sides a, b, and c, and angle A opposite side a, the following equation holds:

c^2 = a^2 + b^2 - 2ab * cos(A)

In our case, we can consider triangle ABD, where AB is side a, AD is side b, and angle A is angle A. We can rearrange the equation to solve for AB:

AB^2 = AD^2 + BD^2 - 2 * AD * BD * cos(A)

Since we know the values of AD and angle A, we can substitute them into the equation and solve for AB.

Let's calculate the length of AB using the given information:

1. The sum of angles B and C is 360 - 90 - (-90) = 360 degrees.

2. Applying the cosine rule to triangle ABD, we have:

AB^2 = AD^2 + BD^2 - 2 * AD * BD * cos(A)

Substituting the known values:

AB^2 = 12^2 + BD^2 - 2 * 12 * BD * cos(90)

Simplifying further:

AB^2 = 144 + BD^2 - 0

AB^2 = 144 + BD^2

Since we don't have the value of BD, we cannot determine the exact length of AB without additional information.

In conclusion, without the value of BD or any other information about the quadrilateral ABCD, we cannot determine the exact length of AB.