Question

1. a right - triangle has one acute angle that measures 38°. find the measure of the third angle and classify this triangle as scalene, isosceles, or equilateral.
2. an isosceles triangle has two angles that each measures 32°. find the measure of the third angle and classify the triangle as acute, right, or obtuse.
3. an isosceles triangle has one angle that measures 98°. find the measures of the other two angles and classify the triangle as acute, right, or obtuse.
4. a triangle has a base that measures 24 inches and an area of 132 in². find the length of the height of this triangle.
5. a triangle has a height that measures 16 cm and an area of 104 cm². find the length of the base of this triangle.
6. a sailor wishes to make a new sail for his boat. the sail is triangular - shaped and measures 18 ft by 11 ft by 25 ft. calculate the number of square feet of material that will be needed for this sail.
7. the dodsons are planning to paint the outside of their house this spring. the paint can states that 1 gallon of paint will cover 350 ft² of surface. using the dimensions of the house shown in the drawing, calculate the number of gallons of paint (rounded to the nearest gallon) they will need to buy to complete the project. (dont include paint for the doors or windows!)
8. tamekas backyard has three trees that form a small triangle. she is planning to plant a flower garden in this triangular area and must calculate the area in order to buy the correct amount of fertilizer and mulch. she measures the following distances for the three sides of the triangle: 10.5 ft, 8.25 ft, and 5.25 ft. calculate the area of this garden.

square windows are 2.5 ft by 2.5 ft
rectangular windows are 2.5 ft by 6 ft
doors are 3 ft by 6.5 ft

Explanation:

Step1: Recall triangle - angle sum property

The sum of the interior angles of a triangle is 180°. In a right - triangle, one angle is 90°. Given one acute angle is 38°. Let the third angle be \(x\). Then \(x + 90^{\circ}+38^{\circ}=180^{\circ}\).

Step2: Solve for the third angle

\[

$$\begin{align*} x&=180^{\circ}-(90^{\circ} + 38^{\circ})\\ x&=180^{\circ}-128^{\circ}\\ x& = 52^{\circ} \end{align*}$$

\]
Since all three angles (38°, 52°, 90°) are different, the triangle is scalene.

Answer:

The measure of the third angle is 52°, and the triangle is scalene.