Multiple Choice
Which statement proves that triangle is an isosceles right triangle?
2. Trigonometric Functions on Right Triangles
Solving Right Triangles
Multiple Choice
A right triangle has a base of units and the angle opposite the height is . What is the height of the triangle?
A
units
B
units
C
units
D
units
Verified step by step guidance1
Identify the given elements in the right triangle: the base length is 68 units, and the angle opposite the height (which is the side we want to find) is 15 degrees.
Recall that in a right triangle, the sine of an angle is the ratio of the length of the side opposite the angle to the hypotenuse. However, here we have the base (adjacent side) and want the height (opposite side), so we can use the tangent function instead.
Write the tangent function for the 15° angle: \(\tan(15^\circ) = \frac{\text{height}}{\text{base}}\).
Substitute the known base length into the equation: \(\tan(15^\circ) = \frac{\text{height}}{68}\).
Solve for the height by multiplying both sides by 68: \(\text{height} = 68 \times \tan(15^\circ)\).
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