Question

please help. trigonometry and Pythagoras question. figure out how much fence is needed. photo attached.

Answer 1

Explanation:

first of all, remember, the sum of all angles in a triangle is always 180°.

so, we know all 3 angles :

90°

53°

180 - 90 - 53 = 37°

and now we use the law of sine to get the other side lengths.

a/sin(A) = b/sin(B) = c/sin(C)

a, b, c are the sides.

A, B, C are the corresponding opposite angles.

so, we have here

126/sin(37) = b/sin(53) = c/sin(90) = c

that means the long side (opposite of the 90° angle) is c and is

c = 126/sin(37) = 209.3666578... m

and from

b/sin(53) = c

we get

b = c×sin(53) = 167.2076475... m

we need as much fence as the sum of all 3 sides (perimeter) :

126 + 167.2076475... + 209.3666578... = 502.5743053... m

one meter costs £1.24

so, the complete fence costs

so, the complete fence costs1.24 × 502.5743053... = £623.1921386... ≈ £623

in my opinion it would be better to round up to the next pound to cover the extra fraction of a meter and to have some wiggle room for some error.

that would mean then £624. but that's not what the problem text is asking for.

Answer 2

£ 433

Explanation:

to find the base of the triangle, we can use Cosine

Cos53 = b/126

b = 75.8

to find the hypotenuse, use Pythagoras' theorem

c² = a² + b²

c² = (75.8)² + 126²

c = 147

a + b + c = 126 + 75.8 + 147 = 348.8

348.8 x £1.24 = 432.512