b To find the height of the prism we should write an expression for its volume and equate it with 600. The area of the prism is the base multiplied by its height. Since the base is a right triangle where a leg and hypotenuse are known, we can find the length of the second leg by using the Pythagorean Theorem.
The short leg of the triangular base is 8 units, which we can use to calculate the area of the prism's base. If we multiply this by the height we obtain an expression for the volume.
V=(1/2* 8* 15)h ⇔ V=60h
Finally, we will equate the expression for the prism's volume with its volume and solve for h.
c The surface area is the sum of the prism's external faces. From Part B, we know that the prism has a height of 10 cm. We also know the second leg of the base.
We know the area of the bases. Additionally, the prism has three rectangular sides. Since we know their dimensions, we can calculate their combined area by adding the product of their length and width.
Sides: 8* 10+15* 10+17* 10 = 400 cm^2
By adding the area of the sides with the bases, we can find the total surface area.
Surface area: 400+60+60=520 cm^2
d We already know that one angle is a right angle. We also know all sides of the triangle. This means we can use either the sine, cosine, or tangent ratio to calculate the triangle's angles.
Let's solve for a and b in these equations.
sin a = 8/17 ⇔ a ≈ 28^(∘) [1em]
sin b = 15/17 ⇔ b ≈ 62^(∘)
The angles are 90^(∘), 28^(∘), and 62^(∘).
