Let’s solve each problem step by step, using the definitions of
opposite leg,
adjacent leg, and
hypotenuse in a right triangle relative to angle θ.
---
🔑 Key Definitions:
-
Hypotenuse: The side *opposite the right angle* — always the longest side.
-
Opposite leg: The side *opposite* angle θ (not touching θ).
-
Adjacent leg: The side *next to* angle θ that is *not* the hypotenuse.
---
##
✔ Problem 1)
Triangle: Right angle at X. Angle θ at Y.
-
Leg opposite to θ: The side *across from* angle Y → that’s
XZ
-
Leg adjacent to θ: The side *next to* angle Y that’s not hypotenuse → that’s
XY
-
Hypotenuse: Side opposite right angle (at X) → that’s
YZ
> ✔️ Answers:
> - Opposite:
XZ
> - Adjacent:
XY
> - Hypotenuse:
YZ
---
##
✔ Problem 2)
Triangle: Right angle at V. Angle θ at U.
-
Opposite to θ (U): Side across from U →
VW
-
Adjacent to θ (U): Side next to U, not hypotenuse →
UV
-
Hypotenuse: Opposite right angle (at V) →
UW
> ✔️ Answers:
> - Opposite:
VW
> - Adjacent:
UV
> - Hypotenuse:
UW
---
##
✔ Problem 3)
Triangle: Right angle at S. Angle θ at R.
-
Opposite to θ (R): Side across from R →
ST
-
Adjacent to θ (R): Side next to R, not hypotenuse →
RS
-
Hypotenuse: Opposite right angle (at S) →
RT
> ✔️ Answers:
> - Opposite:
ST
> - Adjacent:
RS
> - Hypotenuse:
RT
---
##
✔ Problem 4)
Triangle ABC: Right angle at B. Angle θ at A.
Sides given: AB = 35, BC = 12, AC = 37
-
Opposite leg to θ (A): Side across from A →
BC = 12
-
Adjacent leg to θ (A): Side next to A, not hypotenuse →
AB = 35
-
Hypotenuse: Opposite right angle (B) →
AC = 37
> ✔️ Answers:
> - Opposite:
12
> - Adjacent:
35
> - Hypotenuse:
37
---
##
✔ Problem 5)
Triangle LMN: Right angle at M. Angle θ at L.
Sides given: LM = 15, MN = 8, LN = 17
-
Opposite leg to θ (L): Side across from L →
MN = 8
-
Adjacent leg to θ (L): Side next to L, not hypotenuse →
LM = 15
-
Hypotenuse: Opposite right angle (M) →
LN = 17
> ✔️ Answers:
> - Opposite:
8
> - Adjacent:
15
> - Hypotenuse:
17
---
## 📝 Final Answer Summary:
1)
- Opposite:
XZ
- Adjacent:
XY
- Hypotenuse:
YZ
2)
- Opposite:
VW
- Adjacent:
UV
- Hypotenuse:
UW
3)
- Opposite:
ST
- Adjacent:
RS
- Hypotenuse:
RT
4)
- Opposite:
12
- Adjacent:
35
- Hypotenuse:
37
5)
- Opposite:
8
- Adjacent:
15
- Hypotenuse:
17
---
✔ All answers are based on standard trigonometric definitions in right triangles. Always identify the right angle first, then locate angle θ, and apply “opposite”, “adjacent”, and “hypotenuse” accordingly.
Parent Tip: Review the logic above to help your child master the concept of is it a right triangle worksheet.
