MO MAP Geometry Similarity, Right Triangles, and Trigonometry Practice

Similarity, Right Triangles, and Trigonometry skills

Understand similarity in terms of similarity transformations

Prove theorems involving similarity

Define trigonometric ratios in right triangles

Use trigonometric ratios and the Pythagorean theorem to solve right triangles

Standards basis

Missouri Learning Standards (Mathematics K-5 and Mathematics 6-12; revised standards approved April 19, 2016) — Missouri

How the MO MAP reports it

Missouri’s MAP math is built from the Missouri Learning Standards and the state’s item specifications, not from a separate national testing framework. The standards are closely CCSS-aligned in structure, with grade-level and course-level domains used as the native reporting/coverage structure.

Blueprint & weighting

Missouri publishes grade-level and EOC blueprints, but the accessible official pages in this pass did not expose the domain-by-domain percentage tables. The assessment page states that item specifications organize expectations by domains/strands and that blueprints are available for grade-level and EOC assessments.

Official sources

Missouri Department of Elementary and Secondary Education — Missouri Learning Standards
Missouri Department of Elementary and Secondary Education — Mathematics
Missouri Department of Elementary and Secondary Education — Assessment

8 free questions · 0/0 correct

Practice playeasy

In a right triangle, $\sin\alpha = \dfrac{7}{25}$ and $\cos\alpha = \dfrac{24}{25}$ . What is $\tan\alpha$ ?

$\tan\alpha = \dfrac{\sin\alpha}{\cos\alpha} = \dfrac{\dfrac{7}{25}}{\dfrac{24}{25}} = \dfrac{7}{25} \cdot \dfrac{25}{24} = \dfrac{7}{24}$ .

Practice playeasy

In a $30$ - $60$ - $90$ triangle the short leg is $3$ . What is the hypotenuse?

The hypotenuse is twice the short leg: $2 \times 3 = 6$ .

Practice playeasy

In the standard coordinate plane, how many points are both $5$ units from the origin and also exactly $3$ units from the line $x = 0$ ?

Points $5$ units from the origin satisfy $x^{2} + y^{2} = 25$ . Being exactly $3$ units from $x = 0$ means $|x| = 3$ , so $x = 3$ or $x = -3$ . Substituting gives $y^{2} = 16$ , so $y = 4$ or $y = -4$ for each $x$ -value. That yields $(3, 4)$ , $(3, -4)$ , $(-3, 4)$ , and $(-3, -4)$ : $4$ points.

Practice playeasy

A $7$ -foot-tall basketball hoop casts a shadow $14$ feet long. At the same time, a brick chimney casts a shadow $20$ feet long. How tall is the chimney, in feet?

Set up $\dfrac{7}{14} = \dfrac{h}{20}$ . Cross-multiply: $14h = 140$ , so $h = 10$ feet.

Practice playeasy

In a right triangle, $\sin\theta = \dfrac{12}{13}$ and $\tan\theta = \dfrac{12}{5}$ . What is $\cos\theta$ ?

$\cos\theta = \dfrac{\sin\theta}{\tan\theta} = \dfrac{\dfrac{12}{13}}{\dfrac{12}{5}} = \dfrac{12}{13} \cdot \dfrac{5}{12} = \dfrac{5}{13}$ .

Practice playeasy

In a $45$ - $45$ - $90$ triangle one leg is $15$ . What is the other leg?

Both legs of a $45$ - $45$ - $90$ triangle are equal, so the other leg is $15$ .

Practice playeasy

Parallel lines $m$ and $n$ are cut by a transversal. At one intersection, an angle measures $115^{\circ}$ . What is the measure of the corresponding angle at the other intersection?

When parallel lines are cut by a transversal, corresponding angles are congruent. The corresponding angle at the second intersection also measures $115^{\circ}$ .

Practice playmedium

A student who is $4$ feet tall casts a shadow $5$ feet long. A building casts a shadow $65$ feet long at the same time. How tall is the building, in feet?