4. A rectangle has a diagonal of 8 cm. The diagonal creates a 60° angle at the base of the rectangle.

Mathematics

1 answer:

tamaranim1 [39]3 years ago

7 0

9514 1404 393

Answer:

a) see attachment

b) base: 4, height: 4√3

c) area: 16√3

Step-by-step explanation:

a) The figure is drawn in the attachment

b) The side lengths of a 30-60-90 right triangle have the ratio ...

1 : √3 : 2

Multiplying these by 4 gives the side lengths of each triangle created by the diagonal. The base (short leg) is 4 units; the height (long leg) is 4√3 units.

c) The area is the product of base and height:

A = bh

A = 4(4√3) = 16√3 . . . . square units

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Two airplanes leave an airport at the same time, the first headed due north and the second at a bearing of N42^ E . At 2:00PM, t

Leno4ka [110]

Answer:

The two airplanes are about 330miles apart.

Step-by-step explanation:

The diagram interpreting the question has been attached to this response.

As shown in the diagram,

i. the airplanes leave at point C.

ii. at 2.00pm the first and second airplanes are at points A and B respectively, where they are 312miles and 487miles away from the starting point C in directions due north and N42E from the point C.

iii. the points A, B and C form a triangle with sides a, b and c.

To solve for the value of c which is the distance between the two planes at 2.00pm, the cosine rule is used.

c² = a² + b² - 2abcosC --------------(i)

where;

b = 312miles

a = 487miles

C = 42°

Substitute these values into equation (i) and solve as follows;

c² = (487)² + (312)² - 2(312)(487)cos(42)

c² = (237169) + (97344) - 303888cos(42)

c² = (237169) + (97344) - 303888(0.7431)

c² = 334513 - 225819.1728