Lauren drew a triangle. Its sides were 7\text{ mm}7 mm7, start text, space, m, m, end text, 9\text{ mm}9 mm9, start text, space, m, m, end text, and 7\text{ mm}7 mm7, start a text, space, m, m, end text. It has three acute angles.

The triangle has two angles of 49.99° and one angle of 80.02°

Step-by-step explanation:

We have a triangle with sides of 7mm, 9mm and 7mm

The triangle has two equal sides, so this means that this is a Isosceles triangle.

The angles are

The base of this triangle is the side with 9mm, and the two base angles are equal.

We can find the base angles by drawing a line from the middle of the base to the top vertice, then we will have a triangle rectangle with a hypotenuse of 7mm, a adjacent cathetus of 4.5 mm, and with this two things we can find the base angle by using the relation

cos(a) = adjacent cathetus/hypotenuse = 4.5mm/7mm

a = Acos(4.5/7) = 49.99°

Then in our isosceles triangle we have two base angles of 49.99°

To find the other angle we can use the fact that the 3 inner angles of a triangle adds up top 180°

Then

49.99° + 49.99° + A = 180°

A = 180° - 2*49.99° = 80.02°

the answer is b.

step-by-step explanation:

by the trigonometric ratio tangent, tangent equals opposite divided by adjacent.

therefore, tan(50) equals ac/3

multiply each side by 3 to get: ac=3tan(50)

the answer is b.

the sum of the lengths of any two sides of a triangle is greater than the length of the third side. if you take the three sides of a triangle and add them in pairs, the sum is greater than (not equal to) the third side. if that is not true, then it is not possible to construct a triangle with the given side lengths.

step-by-step explanation: