What angle does the rod make with the vertical…

What angle does the rod make with the vertical edge?

Question 19

MediumOriginal question

A hall's corner is the origin $O$ , with the floor edges along the $x$ - and $y$ -axes and the vertical edge along the $z$ -axis; lengths are in metres. A straight rod runs from $O$ to the point $P(6, 2, 9)$ .

What angle does the rod make with the vertical edge?

\cos^{-1}{\left(\frac{9}{11} \right)}

Correct answerYour answer

\sin^{-1}{\left(\frac{9}{11} \right)}

Correct answerYour answer

\cos^{-1}{\left(\frac{6}{11} \right)}

Correct answerYour answer

\cos^{-1}{\left(\frac{2}{11} \right)}

Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer A

Correct answer: A

The vertical edge is the $z$ -axis, and the rod's direction cosine for it is $n = \frac{9}{11}$ .
The angle is $\cos^{-1}\frac{9}{11}$ .

Worth noting

$\sin^{-1}\frac{9}{11}$ treats $\frac{9}{11}$ as a sine; a direction cosine is the cosine of the angle.

Concept: The angles a line makes with the axes
Typical timeTypical: 120 s
Your timeYours: —

The rule this testsDirection cosines of a line

Practise this chapter →

Ten questions from Three-Dimensional Geometry, at your own pace.

Practise this chapter →

Ten questions from Three-Dimensional Geometry, at your own pace.

What angle does the rod make with the vertical edge?

Question 19

Explanation