Triangle Basics — “Trig or Pythagorean"
A right triangle has legs of 3 cm and 4 cm. You need to find the hypotenuse.
→ Do you use Trig or the Pythagorean Theorem?
Pythagorean Theorem — both legs are known, and you’re finding the hypotenuse.
Define sine, cosine, and tangent for an acute angle in a right triangle.
sin=opp/hyp
cos = adj/hyp
tan = opp/adj
Find the hypotenuse of a triangle with legs 9 cm and 12 cm.
15 cm
A right triangle has a leg of 8 cm and a hypotenuse of 10 cm. You need to find one of the acute angles.
→ Do you use Trig or the Pythagorean Theorem?
Trig — use sine, cosine, or tangent to find the angle.
If sin A = 4/5, what sides of the triangle does this represent?
Opposite = 4, Hypotenuse = 5
Find the missing leg if hypotenuse = 13 cm and one leg = 5 cm.
12 cm
You know one leg and the hypotenuse, and you need to find the missing leg.
→ Trig or Pythagorean Theorem?
Either could work, but Pythagorean is more direct if finding the side.
Write a trig equation for finding the angle in a right triangle where the opposite side is 6 and adjacent is 10.
tan θ = 6/10
Find the angle when opposite = 7 cm and adjacent = 24 cm.
θ = tan⁻¹(7/24)
θ≈ 16°
You know one side length and one acute angle (not 90°). You need to find another side.
→ Trig or Pythagorean Theorem?
Trig — you need sine, cosine, or tangent because not all sides are known.
In a triangle, cos x = 0.6. What ratio of sides does this describe?
Adjacent / Hypotenuse = 0.6
Find the height of a tree if its shadow is 20 m long and the angle of elevation to the top is 35°.
h = 20 tan 35°
h≈ 14.0 m
A ladder leans against a wall forming a right triangle with the ground. You know the height the ladder reaches and the angle it makes with the ground. Find the ladder’s length.
→ Trig or Pythagorean Theorem?
Trig — use cosine or sine depending on which side is known.
A triangle has sin A = 0.6428. Estimate the measure of angle A.
A ≈ 40°
Find all side lengths of a triangle if one angle = 25°, hypotenuse = 18.
opp = 18 sin 25° opp≈ 7.6,
adj = 18 cos 25° ≈ 16.3
You’re designing a wheelchair ramp that rises 2.5 feet over a distance of 10 feet. The ramp will also have a handrail that extends diagonally from the top of the ramp to the ground.
Which method should you use to find the length of the handrail — Trig or the Pythagorean Theorem — and why?
Then, calculate the handrail’s length.
Pythagorean Theorem — two sides of the right triangle are known (2.5 ft rise, 10 ft run).
Handrail = √(2.5² + 10²) ≈ 10.3 ft.
In a right triangle, angle A = 32°, and the adjacent side is 9 m.
a) Write a trig equation to find the hypotenuse.
b) Solve for the hypotenuse and round to the nearest tenth.
a) cos(32°) = 9 / h
b) h = 9 / cos(32°) ≈ 10.6 m