Find the diagonal in this rectangular prism 4 yd, 3 yd, 12 yd

1) The shortest distance between the tip of the cone and its rim is going to be a hypotenuse of the right triangle, you can see on the picture.

hypotenuse = adjacent leg *cos α,

α = 77/2 = 38.5⁰.

hypotenuse = 40 /cos 38.5⁰= 51.1 cm

Answer is D. 51.1.

2) To find R, we need to use the law of cosine.

c² = a² + b² - 2ab*cos C.

In our case, c=R,

a=BC=38 N, b= AC=40 N, m∠C=180 - 50=130⁰

R² = 38² + 40² -2*38*40*cos(130⁰) ≈ 4998.0743

R = √4998.0743 ≈ 70.7

Answer is 70.7 N.

3) We can use the law of sine here.

a/sin A = b/sin B = c/sin C.

We need a/sin A = b/sin B for this problem.

b= |AC|=15cm, m∠B=68⁰, a=|BC| =?, m∠A=180-(68+24)= 88⁰

a/sin A = b/sin B

|BC|/sin 88⁰ = 15/sin 68⁰

|BC| = 15*sin(88⁰)/sin(68⁰)= 16.17 cm

Answer is D.16.17 cm.

4) Cosine Law: c²=a²+ b² -2ab*cosC

Answer is C.

area of square c²=area of square a² + area of square b² - area of defect 1 - area of defect 2