Question

Tamika leans a 30-foot ladder against a wall so that it forms an angle of 65∘ with the ground. How high up the wall does the ladder reach? Round your answer to the nearest hundredth of a foot if necessary.

Answer 1

27.19 feet

Explanation:

sin 65=

hypotenuse

opposite

​

=

30

x

​

sin , 65, equals, start fraction, x, divided by, 30, end fraction

sin 65=

30

x

​

start fraction, sin , 65, divided by, 1, end fraction, equals, start fraction, x, divided by, 30, end fraction

1

sin 65

​

=

30

x

30, sin , 65, equals, x

30 sin 65=

x

x, equals, 27, point, 1, 8, 9, 2, 3, 3, point, point, point, approximately equals, 27, point, 1, 9

x=27.189233...≈27.19

The ladder reaches 27.19 feet up the wall.

The ladder reaches 27.19 feet up the wall.

Answer 2

64.34 feet.

Explanation:

To solve this problem, we can use trigonometric ratios, specifically the tangent ratio.

Let's denote the height up the wall that the ladder reaches as "h". We can then set up the following equation:

tan(65°) = h/30

To solve for h, we can multiply both sides by 30:

30 tan(65°) = h

Using a calculator, we can find that tan(65°) is approximately 2.1445. Multiplying this by 30 gives us:

h ≈ 64.34 feet

Therefore, the ladder reaches approximately 64.34 feet up the wall. Rounded to the nearest hundredth of a foot, the answer is 64.34 feet.