Question

I need the answers to these problems for my test corrections.

Answer 1

Answer:

1.   y = 12

    x = 7.9

2.  AB = 5

    AC = 5√3

Step-by-step explanation:

1. If you call the straight up line of both triangles is z, then

(9 + 7)^2 = y^2 + z^2

=> z^2 = 256 - y^2

x^2 + 7^2 = z^2

=> z^2 = x^2 + 49

so 256 - y^2 = x^2 + 49

x^2 = 207 - y^2

for the left smaller triangle: 9^2 + x^2 = y^2

y^2 = x^2 + 81

Substitute:

y^2 = (207 - y^2) + 81

2y^2 = 288

y^2 = 144

y = 12

x^2 = 207 - y^2 = 207 - 144 = 63

x = 7.9

2. Sin(30) = AB/BC

=> AB = BC x sin(30) = 10 x 0.5 = 5

Cos(30) = AC/BC

=> AC = BC x cos(30) = 10 x √3/2 = 5√3