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
