Lesson · Grade 10 · Foundations of Mathematics and Pre Calculus
Solving a Right Triangle: Pythagoras and Trig
- Grade 10
- Foundations of Mathematics and Pre Calculus
- 2 min 11 s
- British Columbia
- BC10-MA-39
A right triangle with legs of 7 cm and 24 cm is solved step by step: the Pythagorean theorem gives the hypotenuse of 25 cm, inverse tangent gives angle A ≈ 16.3°, and the angle sum gives B ≈ 73.7°, with a panel showing the three primary trig ratios and which tool to use for what you know. It then shows the common mistake of rounding 7 ÷ 24 to 0.3 too early, which puts both angles 0.4° off, checks c = 7 ÷ sin A = 25 cm, and ends on the recap: pick the tool from what you know and round only at the end.
Concept: Solving a right triangle with trig and the Pythagorean theorem
Anyone can watch two lessons on the website without an account. Signing in is free, no payment and no card, and opens three a day; Plus has no limit.
Loading
In one sentence
The question this lesson answers
To solve this right triangle, find its missing side and angles. Its legs, the sides at the right angle, are 7 and 24 centimetres.
The hypotenuse, c, faces the right angle. From angle A, the opposite leg faces A, and the adjacent leg touches A.
Transcript
What the lesson says
To solve this right triangle, find its missing side and angles. Its legs, the sides at the right angle, are 7 and 24 centimetres.
The hypotenuse, c, faces the right angle. From angle A, the opposite leg faces A, and the adjacent leg touches A.
The primary trig ratios: sine is opposite over hypotenuse, cosine is adjacent over hypotenuse, and tangent is opposite over adjacent.
Pick the tool from what you know. Two sides, find a side: the Pythagorean theorem. A side and an angle, find a side: a trig ratio. Two sides, find an angle: an inverse trig ratio.
Two sides are known, so use the Pythagorean theorem: c squared is 7 squared plus 24 squared.
That is 49 plus 576, or 625, and its square root is 25 centimetres.
For angle A, we know the opposite and adjacent legs, so use tangent: tan A is 7 divided by 24.
Inverse tangent turns that ratio back into an angle: 16.26 degrees, or about 16.3.
The angles add to 180 degrees, so B is 90 minus the full value of A: about 73.7.
A common mistake is rounding too early. Round 7 divided by 24 to 0.3, and A becomes 16.7 degrees and B 73.3.
Both are off by 0.4 degrees. Keep every digit until the last step.
Check with a side and an angle: sine A is 7 divided by c, so c is 7 divided by sine A, which is 25 centimetres again.
Solved. Pick the tool from what you know, and round only at the end.
Curriculum
Where this fits
- British Columbia, Grade 10
Foundations of Mathematics and Pre Calculus 10, Trigonometry: primary trigonometric ratiosBC10-MA-39
Previous: Angles of Elevation and Depression: Measuring What You Cannot Reach
The outcomes and strands follow the British Columbia curriculum.
Keep going
2 min 3 sAngles in Standard Position and Reference Angles
Grade 11 · 2 min 3 s
2 min 12 sAngles of Elevation and Depression: Measuring What You Cannot Reach
Grade 10 · 2 min 12 s
2 min 3 sExact Values from the Special Triangles
Grade 11 · 2 min 3 s
2 min 23 sFinding a Missing Angle with Inverse Tan
Grade 10 · 2 min 23 s
2 min 11 sFinding a missing side with a trig ratio
Grade 10 · 2 min 11 s
1 min 45 sNaming the Sides of a Right Triangle: Hypotenuse, Opposite, Adjacent
Grade 10 · 1 min 45 s
2 min 13 sSine, cosine and tangent: the three trig ratios
Grade 10 · 2 min 13 s
2 min 6 sSolving Trigonometric Equations from 0° to 360°
Grade 11 · 2 min 6 s
- All Grade 10 Foundations of Mathematics and Pre Calculus lessons
- Create a free account to watch three lessons a day, no payment and no card.