# trig

The lengths of 2 adjacent sides of a parallelogram are 42 cm and 36cm. an angle of the parallelogram is 4o degrees. Find the measure of the longest diagonal to the nearest tenth of a centimeter.

1. 👍
2. 👎
3. 👁
1. The longest diagonal forms a triangle with 180°-40°=140° and adjacent sides of 42 and 36 cm.

Using the cosine rule:
C²=A²+B²-2ABcos(α)
=42²+36²-2*42*36*cos(140°)
=1764+1296-3024(-.766044443)
=5376.52 approx.
C=sqrt(5376.52)
=73.32 cm (approx.)

1. 👍
2. 👎

## Similar Questions

1. ### Math

Note: Enter your answer and show all the steps that you use to solve this problem in the space provided. The figure shows two right trapezoids. Trapezoid A B C D has right angles at B and C. Angle B is adjacent to the shorter

2. ### oblique triangle trigonometry

A parking lot has the shape of a parallelogram. The lengths of two adjacent sides are 70meters and 100meters. The angle between the two sides is 70o. What is the area of the parking lot?

3. ### hhs

Instructions:Drag the tiles to the boxes to form correct pairs. Not all tiles will be used. Match each set of vertices with the type of quadrilateral they form. Tiles A(2, 0), B(3, 2), C(6, 3), D(5, 1) a parallelogram with

4. ### Geometry

Based on the information in the diagram, can you prove that the figure is a parallelogram? Explain. a. Yes; opposite sides are congruent. b. Yes; opposite angles are congruent. c. No; you cannot prove that the quadrilateral is a

1. ### math

Which quadrilaterals have a)perpendicular diagonals b)opposite angles congruent? c) two pairs of parallel sides? d) a pair of congruent, adjacent sides? My answers a)rhombus and square b)rhombus, square, and parallelogram

2. ### Geometry

Can the following quadrilateral be proven to be a parallelogram based on the given​ information? No. It is not a parallelogram because the angles of the quadrilateral do not add up to 360 degrees360°. B. No. It is not a

3. ### Pre-Calculus

A parallelogram has adjacent sides 7 cm and 15 cm. If the shorter diagonal is 10 cm long, find the length of the longer diagonal.

4. ### geometry

Divers looking for a sunken ship have defined the search area as a triangle with adjacent sides of lengths 2.75 and 1.32 the angle between the sides is 35 degrees. find the search area.

1. ### Math

On a centimeter dot array, draw all possible rectangles with a perimeter of 12 cm and sides whose lengths are whole centimeters. Label the lengths of two adjacent sides of each rectangle.

2. ### General Calculus

Let θ (in radians) be an acute angle in a right triangle and let x and y, respectively, be the lengths of the sides adjacent to and opposite θ. Suppose also that x and y vary with time. At a certain instant x=7 units and is

3. ### Math

Prove that an exterior angle of a triangle is equal to the sum of the non adjacent interior angles of that triangle. Use the following variables in your proof. Exterior angle=w Interior adjacent angle= x Interior non adjacent

4. ### geometry

The measure of an angle of a parallelogram is 12 degrees less than 3 times the measure of an adjacent angle. find the measure of all the interior angels of the parallelogram.