Chapter 6: Problem 6
The directed line segment whose initial point is the origin is said to be in ________ ________ .
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Chapter 6: Problem 6
The directed line segment whose initial point is the origin is said to be in ________ ________ .
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In Exercises 75-78, find the component form of the sum of \(\mathbf{u}\) and \(\mathbf{v}\) with direction angles \(\mathbf{\theta_u}\) and \(\mathbf{\theta_v}\). Magnitude ||\(\small{\mathbf{u}}\)|| \(= 4\) ||\(\small{\mathbf{v}}\)|| \(= 4\) Angle \(\mathbf{\theta_u} = 60^{\circ}\) \(\mathbf{\theta_v} = 90^{\circ}\)
The Law of Cosines can be used to establish a formula for finding the area of a triangle called ________ ________ Formula.
GLIDE PATH A pilot has just started on the glide path for landing at an airport with a runway of length 9000 feet. The angles of depression from the plane to the ends of the runway are \(17.5^{\circ}\) and \(18.8^{\circ}\). (a) Draw a diagram that visually represents the situation. (b) Find the air distance the plane must travel until touching down on the near end of the runway. (c) Find the ground distance the plane must travel until touching down. (d) Find the altitude of the plane when the pilot begins the descent.
In Exercises 53-58, determine whether \(\mathbf{u}\) and \(\mathbf{v}\) are orthogonal, parallel, or neither. \(\mathbf{u} = \langle 3, 15 \rangle\) \(\mathbf{v} = \langle -1, 5 \rangle\)
HEIGHT A flagpole at a right angle to the horizontal is located on a slope that makes an angle of \(12^{\circ}\) with the horizontal. The flagpole's shadow is 16 meters long and points directly up the slope. The angle of elevation from the tip of the shadow to the sun is \(20^{\circ}\). (a) Draw a triangle to represent the situation. Show the known quantities on the triangle and use a variable to indicate the height of the flagpole. (b) Write an equation that can be used to find the height of the flagpole. (c) Find the height of the flagpole.
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