Answer:
1. 29.44 feet.
2. 2/3.
3. 10/9.
4. 39/5.
Step-by-step explanation:
1. 34-foot ladder makes a 60 degree angle with the ground. If you visualize a 30-60-90 triangle with the ladder and the building and the ground, you can see that the hypotenuse of the triangle is 34 feet.
With 30-60-90 triangles, the short side is x, the hypotenuse is 2x, and the long side is x and the square root of 3.
If the hypotenuse is 34 feet, that must mean that the short side is 34 / 2 = 17 feet. The long side will be 17 * sqrt(3) = 17 * 1.732050808 = 29.44486373. So, the height above the ground will be about 29.44 feet.
2. Tangent of A! For this, we will use SOH CAH TOA... TOA stands for tangent: opposite over adjacent.
According to the diagram, angle A has an adjacent side of 15 units and an opposite side of 10 units. That means that tanA = 10 / 15 = 2/3.
If you want to find the measure of angle A, you can easily find the cotangent of 2/3. That is 33.69006753, or about 34 degrees.
3. The ratio should be 5 feet to 54 inches. There are 12 inches in 1 foot, so 5 feet is the same thing as 60 inches. 60 / 54 = 30 / 27 = 10/9.
4. (p + 9) / 7 = 12 / 5
5(p + 9) = 12 * 7
5p + 45 = 84
5p = 39
p = 7.8
That is the same thing as 7 and 4/5, or (35 + 4)/5 = 39/5
Really hope this helps!!
