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Chapter 6: Problem 35

The three given points are the vertices of a triangle. Solve each triangle, rounding lengths of sides to the nearest tenth and angle measures to the nearest degree. $$A(0,0), B(-3,4), C(3,-1)$$

Short Answer

Expert verified
The rounded lengths of the sides and the rounded measurements of the angles for the given vertices of the triangle will be the required solution.

Step by step solution

01

Calculate the Lengths of the Sides

Using the distance formula: \[d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}\]calculate the distances between each pair of points:AB = \(\sqrt{(-3-0)^2 + (4-0)^2}\)BC = \(\sqrt{(3+3)^2 + (-1-4)^2}\)AC = \(\sqrt{(3-0)^2 + (-1-0)^2}\)
02

Rounding Off the Lengths

Round off each of the distances calculated in step 1 to the nearest tenth.
03

Calculate the Angles

The cosine of an angle A in a triangle can be calculated using the law of cosines: \[cosA = \frac{b^2 + c^2 - a^2}{2bc}\]where \(a, b, c\) are the sides of the triangle as calculated in step 1, and a is the side opposite angle A. Calculate the cosine for each angle, and obtain the angle measurements by applying the inverse cosine function: \[A = arccos(cosA) \] and likewise for the other angles.
04

Rounding Off the Angles

Round off each of the angles calculated in step 3 to the nearest degree.

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Most popular questions from this chapter

Use the dot product to determine whether v and w are orthogonal. $$\mathbf{v}=2 \mathbf{i}-2 \mathbf{j}, \quad \mathbf{w}=-\mathbf{i}+\mathbf{j}$$

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