# Expression of a variable from the formula + triangle - practice problems

#### Number of problems found: 712

- Opposite 78434

We see the tree on the opposite bank of the river at an angle of 15° from a distance of 41m from the river bank. From the bank of the river, we can see at an angle of 31°. How tall is the tree? - One-third 77724

The cuboid has a body diagonal u=25 cm, and side b is one-third longer than side a. What is the volume of the cuboid? - Angles in a triangle

In a triangle, the first angle measures a number plus 45°, and the second angle is 30° less than the first angle. The third angle is two times the number more than the first angle. What are the measurements of each angle of the triangle? - Find all

Find all right-angled triangles whose side lengths form an arithmetic sequence. - A triangle 4

A triangle has a perimeter of 18a + 6b + 15 and has sides of lengths 5a + 7 and 8a +4b. What is the length of the third side? Write an expression and simplify it to find the solution to the problem. - A Pile of salt

A Pile of salt has been stored in the shape of a cone. Mr. Terwilliker knows that the pile is 20 feet tall and 102 feet in circumference at the base. What area of the conical tarpaulin (a large sheet of material) is needed to cover the pile? - Solve 13

Solve the missing dimensions for the following triangle: Triangle ABC: AngleA=43 degrees, b=7.0cm, c=6.0cm Question 1. Angle B with units written as degrees Question 2. Angle C with units written as degrees Question 3. a, rounded to the nearest tenth of a - Sin cos tan

If cos y = 0.8, 0° ≤ y ≤ 90°, find the value of (4 tan y) / (cos y-sin y) - The radius

A right circular cone's radius and slant heights are 9 cm and 15 cm, respectively. Find, correct to one decimal place, the (i) Height (ii) Volume of the cone - Calculate 74024

The diagonal of the axial section of the rotating cylinder is 6 cm, and its surface is 30 cm square. Calculate the radius of the base. - Isosceles right triangle

If the square of the hypotenuse of an isosceles right triangle is 128 cm^{2}, find the length of each side. - A construction

A construction worker is trying to find the height of a skyrise building. He is standing some distance away from the base with an angle of elevation of 65 degrees. The worker moves 50 feet closer and measures the angle of elevation to be 75 degrees. Find - Perpendicular 73574

The two lines of the triangle are perpendicular to each other and are 27 cm and 36 cm. Calculate the length of the sides of the triangle and the length of the third line. - Loonie

Loonie has three wooden sticks measuring 17 inches, 21 inches, and 25 inches. He lays them down to form a triangle. Find the measure of the angle enclosed by 17 inches and 21 inches. (Express answers to the nearest hundredths) (using the law of cosines) - Binibini

Binibini owns a triangular residential lot bounded by two roads intersecting at 70°. The sides of the lot along the road are 62m and 43m, respectively. Find the length of the fence needed to enclose the lot. (express answers to the nearest hundredths) - Perpendicular 73264

The perimeter of a right triangle is equal to 30 centimeters. Calculate the perpendicular b if a = 5 centimeters and c = 13 centimeters. A natural number expresses the length of the perpendicular b. - A flagpole

A flagpole is leaning at an angle of 107° with the ground. A string fastened to the top of the flagpole is holding up the pole. The string makes an angle of 38° with the ground, and the flagpole is 8 m long. What is the length of the string? - Calculate 73024

Calculate the permille descent of the railway line in the section of 7.2 km by 21.6 m. - Calculate 72624

The perimeter of the ABC triangle is 19.6 cm. The following applies to the lengths of its sides: a: c = 1:2, b: c = 5:6. Calculate the lengths of all sides of the triangle ABC. - Hypotenuse 72524

We know the height of the hypotenuse h = 4cm and the hypotenuse c = 19cm in a right triangle. How to calculate the segments of legs - sections on the hypotenuse c1, c2

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