Question

Could I possibly have help with this? I don’t really have time and I really need help

Answer 1

By using trigonometric function,

`m \angle B` = 39.8

`m \angle C` = 50.2

The two houses are (represented as d) is approximately 53.169 m apart.

How to find how far apart the houses are

In a right-angled triangle ABC, with angle A as 90 degrees, side AB as 40 m, and side AC as 35 m, n determine the missing angles and side using trigonometric functions.

To find angle B, use the inverse tangent function (
`tan^(-1)`):

angle B =
`tan^-1`(opposite/adjacent) =
`tan^-1`(AC/AB) =
`tan^-1`(35/40)

Using a calculator or trigonometric tables, we find that angle B ≈ 39.805 degrees.

To find angle C, we know that the sum of the angles in a triangle is always 180 degrees. Since angle A is 90 degrees and angle B is approximately 39.805 degrees, we can find angle C:

angle C = 180 - angle A - angle B = 180 - 90 - 39.805 ≈ 50.195 degrees.

Now, to find how far apart the houses are, use the Pythagorean theorem, which states that in a right-angled triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.

Using the Pythagorean theorem, we have:

`BC^2 = AB^2 + AC^2\\d^2 = 40^2 + 35^2`

`d^2` = 1600 + 1225

`d^2` = 2825

Taking the square root of both sides, we find:

d ≈ √2825 ≈ 53.169 m

Therefore, angle B is approximately 39.805 degrees, angle C is approximately 50.195 degrees, and the two houses are (represented as d) is approximately 53.169 m apart.