The ratio of the angle measures of the triangle are 3:1:5.if the longest side of the triangle is 15ft .the shortest side of the triangle is?

≈ 5.2 ft

Step-by-step explanation:

sum the parts of the ratio, 3 + 1 + 5 = 9 parts

Divide the angle sum of a triangle by 9 to find the value of one part of the ratio.

180° ÷ 9 = 20° ← value of 1 part of the ratio, then

3 parts = 3 × 20° = 60°

5 parts = 5 × 20° = 100°

The angles of the triangle are 100°, 60° and 20°

The longest side is opposite the largest angle in the triangle

The shortest side is opposite the smallest angle in the triangle.

Thus

the longest side is opposite 100°

the shortest side is opposite 20°

let x represent the shortest side and using the Sine rule

= ( cross- multiply )

x × sin100° = 15sin20° ( divide both sides by sin100° )

x = ≈ 5.2 ( to the nearest tenth )

Thus the shortest side is ≈ 5.2 ft

associative property hopes this ! : )

step-by-step explanation:

intensity of the vector is v= √37 ≈ 6.08 units and make angle ∡α ≈ 9.46° with east direction

step-by-step explanation:

required vector is consists of the two componentsvx= 2+4=6 units   and vy= 1 unit and vx ⊥ vywe will use pythagorian theorem to find intensity of the vector vv∧2 = vx∧2 + vy∧2 => v = √vx∧2 + vy∧2 = √6∧2 + 1∧2 = √36+1 = √37 ≈ 6.08 unitsthe angle ∡α between vector and east direction we wil find with tanαtanα = 1/6 => α = arc tanα = arc 1/6 => α ≈ 9.46°

hope this