a. The height up the building the ladder reaches can be found using the sine of the angle θ. The sine of an angle in a right triangle is defined as the length of the opposite side (in this case, the height up the building) divided by the length of the hypotenuse (the ladder).

Since we know that tan θ = 3/8, we can find sin θ by using the Pythagorean identity sin^2 θ + cos^2 θ = 1.

First, we find cos θ by using the identity tan θ = sin θ / cos θ, which gives us cos θ = sin θ / tan θ.

Substituting tan θ = 3/8 into the equation gives cos θ = sin θ / (3/8) = 8sin θ / 3.

Substituting cos θ = 8sin θ / 3 into the Pythagorean identity gives (sin^2 θ) + (64sin^2 θ / 9) = 1.

Solving this equation for sin θ gives sin θ = 3/√73.

Finally, the height up the building the ladder reaches is sin θ * length of the ladder = (3/√73) * 10 = 30/√73 ≈ 3.51 meters.

b. The distance from the foot of the ladder to the base of the building can be found using the cosine of the angle θ. The cosine of an angle in a right triangle is defined as the length of the adjacent side (in this case, the distance from the foot of the ladder to the base of the building) divided by the length of the hypotenuse (the ladder).

We already found that cos θ = 8/√73.

So, the distance from the foot of the ladder to the base of the building is cos θ * length of the ladder = (8/√73) * 10 = 80/√73 ≈ 9.35 meters.

Question

a. The height up the building the ladder reaches can be found using the sine of the angle θ. The sine of an angle in a right triangle is defined as the length of the opposite side (in this case, the height up the building) divided by the length of the hypotenuse (the ladder).

Since we know that tan θ = 3/8, we can find sin θ by using the Pythagorean identity sin^2 θ + cos^2 θ = 1.

First, we find cos θ by using the identity tan θ = sin θ / cos θ, which gives us cos θ = sin θ / tan θ.

Substituting tan θ = 3/8 into the equation gives cos θ = sin θ / (3/8) = 8sin θ / 3.

Substituting cos θ = 8sin θ / 3 into the Pythagorean identity gives (sin^2 θ) + (64sin^2 θ / 9) = 1.

Solving this equation for sin θ gives sin θ = 3/√73.

Finally, the height up the building the ladder reaches is sin θ * length of the ladder = (3/√73) * 10 = 30/√73 ≈ 3.51 meters.

b. The distance from the foot of the ladder to the base of the building can be found using the cosine of the angle θ. The cosine of an angle in a right triangle is defined as the length of the adjacent side (in this case, the distance from the foot of the ladder to the base of the building) divided by the length of the hypotenuse (the ladder).

We already found that cos θ = 8/√73.

So, the distance from the foot of the ladder to the base of the building is cos θ * length of the ladder = (8/√73) * 10 = 80/√73 ≈ 9.35 meters.

Knowee AI · Accepted Answer

a. The height up the building the ladder reaches can be found using the sine of the angle θ. The sine of an angle in a right triangle is defined as the length of the opposite side (in this case, the height up the building) divided by the length of the hypotenuse (the ladder).

Since we know that tan θ = 3/8, we can find sin θ by using the Pythagorean identity sin^2 θ + cos^2 θ = 1.

First, we find cos θ by using the identity tan θ = sin θ / cos θ, which gives us cos θ = sin θ / tan θ.

Substituting tan θ = 3/8 into the equation gives cos θ = sin θ / (3/8) = 8sin θ / 3.

Substituting cos θ = 8sin θ / 3 into the Pythagorean identity gives (sin^2 θ) + (64sin^2 θ / 9) = 1.

Solving this equation for sin θ gives sin θ = 3/√73.

Finally, the height up the building the ladder reaches is sin θ * length of the ladder = (3/√73) * 10 = 30/√73 ≈ 3.51 meters.

b. The distance from the foot of the ladder to the base of the building can be found using the cosine of the angle θ. The cosine of an angle in a right triangle is defined as the length of the adjacent side (in this case, the distance from the foot of the ladder to the base of the building) divided by the length of the hypotenuse (the ladder).

We already found that cos θ = 8/√73.

So, the distance from the foot of the ladder to the base of the building is cos θ * length of the ladder = (8/√73) * 10 = 80/√73 ≈ 9.35 meters.

2. A firefighter’s ladder leans against a building. If the ladder is 10 meters long and makes angle with the ground, and tan θ=3/8 ,a. how high up the building does the ladder reach?b. how far away is the foot of the ladder from the base of the building?

Question

Solution

Similar Questions

Upgrade your grade with Knowee