Question

Performance Task Review 1

Answer 1

Answer: a = 5; b = 5; c = 10; d = 5$\sqrt{3}$; e = 5$\sqrt{2}$; f = 6.93; g = 13

$A_{H}$ = 12.5; $A_{J}$ = 55; $A_{K}$ = 12.5$\sqrt{3}$; $A_{L}$ = 38.1

Step-by-step explanation:

Value of e:

sin 45 = $\frac{5}{e}$

e = 5.$\frac{2}{\sqrt{2} }$

e = 5$\sqrt{2}$

Value of a:

e² = 5² + a²

a = $\sqrt{ (5\sqrt{2} )^{2} - 5^{2} }$

a = 5

Value of b:

The figure J is a rectangle, so opposite sides have the same value. Since b is opposite side of the side measuring 5, b = 5.

Value of c:

sin 30 = $\frac{5}{c}$

c = 5. 2

c = 10

Value of d:

cos 30 = $\frac{d}{10}$

d = 10.$\frac{\sqrt{3} }{2}$

d = 5$\sqrt{3}$

Value of g:

cos 56 = $\frac{11}{g}$

g = $\frac{11}{0.8532}$

g = 13

Value of f:

g² = 11² + f²

f = $\sqrt{169 - 121}$

f = 7

Area of H:

$A_{H}$ = $\frac{5.5}{2}$

$A_{H}$ = 12.5

Area of J:

$A_{J}$ = 11.5

$A_{J}$ = 55

Area of K:

$A_{K}$ = $\frac{5\sqrt{3}.5 }{2}$

$A_{K}$ = 12.5$\sqrt{3}$

Area of L:

$A_{L}$ = $\frac{11.7}{2}$

$A_{L}$ = 38.5