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Math help

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• 1.

In order to unload clay easily, the body of a dump truck must be elevated to at least 45°. The body of a dump truck that is 12 feet long has been raised to 8 feet. Will the clay pour out easily?

• 2. Find the area of sector GHJ given that 𝜃 = 40°. Use 3.14 for 𝜋 and round to the nearest tenth.

• 3. What is the area of ∆𝐵𝐶𝐷 to the nearest tenth of a square centimeter?

May 3, 2018

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1. The 12 ft   can be considered the hypotenuse of a right triangle

And the 8 ft  can be considered the leg opposite the angle we are considering

So....to  find out if this angle is at least 45°, we have take thw sine inverse of  8/12

So  we have

asin (8/12)  =  the angle  ≈ 41.8°.....so....it won't pour out smoothly

2. Area  =  (3.14) r^2 *  (40/ 360)  =

(3.14) * 4^2 * 1/9   =

16 * 3.14 / 9    =

5.6 cm^2

3. We have  a 30-60-90  right triangle.....the side opposite the 30 degree angle  = 10 = base

And the side oposite the 60 degree angle  = 10√3 cm = height

So....the area  is   (1/2) base * height  =

(1/2) 10 * 10√3  =

50√3   cm^2  ≈    86.6 cm^2   May 3, 2018