AI Math Solver
Resources
Questions
Pricing
Login
Register
Home
>
Questions
>
Calculate Angle y in a Right-Angled Triangle with Given Leg Lengths
Mathematics
Grade 10 (Junior High School)
Question Content
Calculate the size of angle y. Give your answer to the nearest degree. The triangle is a right-angled triangle with the two legs measuring 11.3 cm and 16.2 cm, and angle y is the angle adjacent to the 11.3 cm leg and opposite to the 16.2 cm leg.
Correct Answer
55°
Detailed Solution Steps
1
Step 1: Identify the sides relative to angle y. The side opposite angle y is 16.2 cm, and the side adjacent to angle y is 11.3 cm.
2
Step 2: Use the tangent trigonometric ratio, which is defined as tan(angle) = opposite/adjacent. Substitute the values: tan(y) = 16.2 / 11.3 ≈ 1.4336.
3
Step 3: Calculate the inverse tangent (arctangent) of 1.4336 to find angle y: y = arctan(1.4336).
4
Step 4: Use a calculator to compute the value, which is approximately 55 degrees when rounded to the nearest whole number.
Knowledge Points Involved
1
Trigonometric Ratios (Tangent)
In a right-angled triangle, the tangent of an acute angle is the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle, written as tan(θ) = opposite/adjacent. It is used to relate the angles of a right triangle to the lengths of its sides.
2
Inverse Trigonometric Functions (Arctangent)
The arctangent function (arctan or tan⁻¹) is the inverse of the tangent function. It is used to find the measure of an acute angle in a right triangle when the ratio of the opposite and adjacent sides is known, i.e., if tan(θ) = x, then θ = arctan(x).
3
Rounding Decimal Degrees
When a calculated angle results in a decimal value, rounding to the nearest degree means looking at the first decimal place: if it is 0.5 or greater, round up the whole number; if it is less than 0.5, keep the whole number as it is.
Loading solution...
