A ladder leaning against a house makes an angle of 65 degrees with the ground. The foot of the ladder is 7 feet from the foot of the house. How long is the ladder? Round to the nearest tenth.
You must learn the trig relationships of a right-angled triangle!
In this case:
cos65° = 7/h
h = 7/cos65° = appr 16.6 m
or sec 65 = h/7
h = 7sec 65 = 7(2.36620...) = 16.6 m
To find the length of the ladder, we can use trigonometry. Specifically, we can use the trigonometric function cosine.
The adjacent side of the triangle is the distance from the foot of the ladder to the foot of the house, which is given as 7 feet.
The angle between the ground and the ladder is 65 degrees. We can use the cosine function to calculate the hypotenuse (length of the ladder).
The cosine of an angle can be found by dividing the length of the adjacent side by the length of the hypotenuse. In this case, it would be:
cos(65 degrees) = adjacent / hypotenuse
Rearranging the equation to solve for the hypotenuse, we have:
hypotenuse = adjacent / cos(65 degrees)
Plugging in the values, we get:
hypotenuse = 7 / cos(65 degrees)
Using a calculator or trigonometric table, we can find the value of cosine of 65 degrees. In this case, it is approximately 0.42262.
So the length of the ladder is:
hypotenuse = 7 / 0.42262 ≈ 16.5627
Rounding to the nearest tenth, the length of the ladder is approximately 16.6 feet.