第9章数学モデルと幾何

What is the supplement of a $\text{48°}$ angle?

What is the complement of a $\text{61°}$ angle?

Two angles are complementary. The smaller angle is $\text{24°}$ less than the larger angle. Find the measures of both angles.

Two angles are supplementary. The larger angle is $\text{45°}$ more than the smaller angle. Find the measures of both angles.

The measures of two angles of a triangle are $22$ and $85$ degrees. Find the measure of the third angle.

One angle of a right triangle measures $41.5$ degrees. What is the measure of the other small angle?

One angle of a triangle is $\text{30°}$ more than the smallest angle. The largest angle is the sum of the other angles. Find the measures of all three angles.

One angle of a triangle is twice the measure of the smallest angle. The third angle is $\text{60°}$ more than the measure of the smallest angle. Find the measures of all three angles.

side $x$

side $b$

Sergio needs to attach a wire to hold the antenna to the roof of his house, as shown in the figure. The antenna is $8$ feet tall and Sergio has $10$ feet of wire. How far from the base of the antenna can he attach the wire?

Seong is building shelving in his garage. The shelves are $36$ inches wide and $15$ inches tall. He wants to put a diagonal brace across the back to stabilize the shelves, as shown. How long should the brace be?

amount of sand in a sandbag

height of a tree

size of a patio

length of a highway

The length of a rectangle is $42$ meters and the width is $28$ meters.

The length of a rectangle is $36$ feet and the width is $19$ feet.

A sidewalk in front of Kathy’s house is in the shape of a rectangle $4$ feet wide by $45$ feet long.

A rectangular room is $16$ feet wide by $12$ feet long.

Find the length of a rectangle with perimeter of $220$ centimeters and width of $85$ centimeters.

Find the width of a rectangle with perimeter $39$ and length $11.$

The area of a rectangle is $2356$ square meters. The length is $38$ meters. What is the width?

The width of a rectangle is $45$ centimeters. The area is $2700$ square centimeters. What is the length?

The length of a rectangle is $12$ centimeters more than the width. The perimeter is $74$ centimeters. Find the length and the width.

The width of a rectangle is $3$ more than twice the length. The perimeter is $96$ inches. Find the length and the width.

Find the area of a triangle with base $18$ inches and height $15$ inches.

Find the area of a triangle with base $33$ centimeters and height $21$ centimeters.

A triangular road sign has base $30$ inches and height $40$ inches. What is its area?

If a triangular courtyard has sides $9$ feet and $12$ feet and the perimeter is $32$ feet, how long is the third side?

A tile in the shape of an isosceles triangle has a base of $6$ inches. If the perimeter is $20$ inches, find the length of each of the other sides.

Find the length of each side of an equilateral triangle with perimeter of $81$ yards.

The perimeter of a triangle is $59$ feet. One side of the triangle is $3$ feet longer than the shortest side. The third side is $5$ feet longer than the shortest side. Find the length of each side.

One side of a triangle is three times the smallest side. The third side is $9$ feet more than the shortest side. The perimeter is $39$ feet. Find the lengths of all three sides.

The height of a trapezoid is $8$ feet and the bases are $11$ and $14$ feet. What is the area?

The height of a trapezoid is $5$ yards and the bases are $7$ and $10$ yards. What is the area?

Find the area of the trapezoid with height $25$ meters and bases $32.5$ and $21.5$ meters.

A flag is shaped like a trapezoid with height $62$ centimeters and the bases are $91.5$ and $78.1$ centimeters. What is the area of the flag?