area
A rectangular garden has a length of 12 meters and a width of 8 meters. There is a circular pond with a diameter of 6 meters located in the center of the garden. What is the total area of the garden
124.26 square meters.
A triangle has legs that has lengths of 6 inches and 8 inches and they form a right angel. What is the length of the last side.
10
A triangle ABC has vertices at A(2,3), B(6,3), and C(4,7) on the coordinate plane.
Reflect triangle ABC over the y-axis. Determine the coordinates of the image vertices and label the triangle A′B′C′.
Therefore, the image triangle A′B′C′ has vertices A′(−2,3), B′(−6,3), and C′(−4,7).
A ladder leans against a wall forming an angle of 60 degrees with the ground. If the ladder is 10 meters long, find the distance of the ladder's bottom from the wall.
draw the picture
5 meters.
an angle the = 90 degree is
right angle
A circular garden has a radius of 15 meters. Surrounding the garden is a rectangular pathway with a width of 5 meters. Find the total area of the garden and the pathway combined.
2306.86m2
In triangle ABC, angle A measures 50 degrees, angle B measures 70 degrees, and the length of side AB is 8 centimeters. What is the measures of the last angel?
60 degrees
A rectangle ABCD has vertices at A(1,2), B(5,2), C(5,6), and D(1,6) on the coordinate plane.
a) Translate rectangle ABCD 3 units to the right and 2 units down. Determine the coordinates of the image vertices and label the rectangle A'′B′C′D′.
Therefore, the image rectangle A′B′C′D′ has vertices A′(4,0), B′(8,0), C′(8,4), and D′(4,4).
In triangle ABC, angle A measures 30 degrees and angle B measures 60 degrees. The length of side AC is 10 meters. Find the length of side AB.
draw the picture
10 square root 3
two angles that add up to 180 degrees are called
supplementary angles
A trapezoid-shaped field has parallel sides of length 20 meters and 30 meters, and a height of 15 meters. Find the area of the field.
375 square meters.
In triangle XYZ, the length of side XY is 10 centimeters, and the length of side YZ is 15 centimeters. If angle X measures 60 degrees, find the length of side XZ to the nearest centimeter.Round to the nearest centimeter,
13 centimeters.
A square WXYZ has vertices at W(1,3), X(4,3), Y(4,6), and Z(1,6) on the coordinate plane.
a) Reflect square WXYZ over the x-axis. Determine the coordinates of the image vertices and label the square W′X′Y′Z′..
Therefore, the image square ′W′X′Y′Z′ has vertices W′(1,−3), X′(4,−3), Y′(4,−6), and Z′(1,−6).
A lighthouse is situated on a cliff that is 50 meters above sea level. From a boat at sea, the angle of elevation to the top of the lighthouse is 20 degrees. Find the distance between the boat and the foot of the lighthouse.
draw the picture
137.36 meters.
two angle that add up to less that 90 degrees
acute
A rectangular room measures 8 meters in length and 6 meters in width. If there is a square rug placed in the center of the room, with each side of the rug measuring 4 meters, find the total area of the room covered by the rug and the remaining floor area.
So, the total area of the room covered by the rug is 16 m 216m2, and the remaining floor area is 32 m 232m2.
Triangle ABC is a right triangle with angle C measuring 90 degrees. Side AC has a length of 6 centimeters, and side BC has a length of 8 centimeters. Find the length of side AB.
the length of side AB is 10 centimeters.
A triangle ABC has vertices at A(2,4), B(5,4), and C(4,7) on the coordinate plane.
a) Reflect triangle ABC over the y-axis. Determine the coordinates of the image vertices and label the triangle A′B′C′.
Therefore, the image triangle A′B′C′ has vertices A′(−2,4), B′(−5,4), and C′(−4,7).
A ladder is leaning against a wall. The ladder is 15 meters long and forms an angle of 60 degrees with the ground. Determine the distance between the base of the ladder and the wall.
draw the picture
So, the distance between the base of the ladder and the wall is 7.5 meters.
79 + X =180 how much is the X worth
A circular swimming pool has a diameter of 10 meters. Surrounding the pool is a path of uniform width. If the width of the path is 2 meters, find the total area of the pool and the path combined. do not leave in terms of pi round 2 decimals places.
153.94m2
Triangle DEF is an isosceles triangle where DE = EF. Angle D measures 70 degrees, and angle E measures 55 degrees. If DE is 12 centimeters long, find the length of side DF.
12 centimeters long.
Consider the triangle ABC with vertices A(-2, 1), B(4, 3), and C(1, -4) in the coordinate plane.
Perform a reflection of triangle ABC over the y-axis. Let's call this reflected triangle A'B'C'.
So, the reflected triangle A'B'C' has vertices A'(2, 1), B'(-4, 3), and C'(-1, -4).
A plane is flying at an altitude of 10,000 meters. From an observer on the ground, the angle of elevation to the plane is 30 degrees. Determine the horizontal distance between the observer and the plane.
draw the picture
17,320 meters.
In triangle ABC, angle A measures 40 degrees, angle B measures 70 degrees, and angle C measures x degrees. Find the measure of angle C.
70∘