Question

Performance Task Review 1

Given the diagram below, find all the values listed in simplified radical form except
for f and g which should be found to the nearest tenth. Show complete work for
obtaining fand g.
a-
=
b=
d-
e
I 8
L
f=
56°
11
5
K
H
d
30°
45°
a

Answer 1

Answer: a = 5; b = 5; c = 10; d = 5
`√(3)`; e = 5
`√(2)`; f = 6.93; g = 13

`A_(H)` = 12.5;
`A_(J)` = 55;
`A_(K)` = 12.5
`√(3)`;
`A_(L)` = 38.1

Explanation:

Value of e:

sin 45 =
`(5)/(e)`

e = 5.
`(2)/(√(2) )`

e = 5
`√(2)`

Value of a:

e² = 5² + a²

a =
`\sqrt{ (5√(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 =
`(5)/(c)`

c = 5. 2

c = 10

Value of d:

cos 30 =
`(d)/(10)`

d = 10.
`(√(3) )/(2)`

d = 5
`√(3)`

Value of g:

cos 56 =
`(11)/(g)`

g =
`(11)/(0.8532)`

g = 13

Value of f:

g² = 11² + f²

f =
`√(169 - 121)`

f = 7

Area of H:

`A_(H)` =
`(5.5)/(2)`

`A_(H)` = 12.5

Area of J:

`A_(J)` = 11.5

`A_(J)` = 55

Area of K:

`A_(K)` =
`(5√(3).5 )/(2)`

`A_(K)` = 12.5
`√(3)`

Area of L:

`A_(L)` =
`(11.7)/(2)`

`A_(L)` = 38.5