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Three simple steps: (1) Share an assignment from thousands of standards-aligned topics using a share code. (2) Students speak and draw their thinking naturally, and Goblins responds with Socratic questioning that sounds just like their teacher. (3) Teachers get real-time formative insights showing what students struggle with and suggestions to inform instruction.

Does Goblins prevent cheating?

Yes. Goblins uses a purpose-trained AI model that evaluates cheating signals in real time. It can detect when students are copying answers, using external tools inappropriately, or not genuinely working through problems. Copy-pasting answers is also blocked.

Can I use my own voice with Goblins?

Yes. Teachers can record their voice and take a selfie to create a custom 3D avatar in about 30 seconds. Students then hear help in their own teacher's voice and see a familiar face, making the experience more personal and effective.

What math levels does Goblins cover?

Goblins covers math from Grade 5 through AP Calculus, including thousands of standards-aligned topics. Teachers can also upload their own content for custom assignments at any level.

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Does Goblins support English Language Learners?

Yes. Goblins supports 30+ languages so teachers don't have to translate every worksheet. It is especially helpful for ELL students who need accessible math instruction in their native language.

What grade level is G-SRT taught?

This standard is part of the G-SRT curriculum in Alaska Mathematics Standards.

G-SRT: Similarity, Right Triangles, and Trigonometry

Similarity, Right Triangles, and Trigonometry

Print

Similarity, Right Triangles, and Trigonometry covers dilations and similarity transformations as the basis for proving triangles similar and understanding scale. The Pythagorean theorem is proved and applied, and trigonometric ratios in right triangles are defined and used to find missing sides and angles. The law of sines and law of cosines extend these tools to non-right triangles.

G-SRT.1Verify experimentally the properties of dilations given by a center and a scale factor:G-SRT.10(+) Prove the Laws of Sines and Cosines and use them to solve problems.G-SRT.11(+) Understand and apply the Law of Sines and the Law of Cosines to find unknown measurements in right and non-right triangles (e.g., surveying problems, resultant forces).G-SRT.2Given two figures, use the definition of similarity in terms of transformations to explain whether or not they are similar.G-SRT.3Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar.G-SRT.4Prove theorems about triangles. Theorems include: a line parallel to one side of a triangle divides the other two proportionally, and conversely.G-SRT.5Apply congruence and similarity properties and prove relationships involving triangles and other geometric figures.G-SRT.6Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles.G-SRT.7Explain and use the relationship between the sine and cosine of complementary angles.G-SRT.8Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.G-SRT.9(+) Derive the formula A = 1/2 ab sin(C) for the area of a triangle by drawing an auxiliary line from a vertex perpendicular to the opposite side.

Example Problems

A sequence of transformations is described below.
1. A reflection over a line

\overleftrightarrow{OP}

2. A dilation about the point P
What must be preserved under this sequence of transformations: angle measures and/or segment lengths?

A sequence of transformations is described below.
1. A translation
2. A rotation about a point A
3. A reflection over a line

\overleftrightarrow{BC}

What must be preserved under this sequence of transformations: angle measures and/or segment lengths?

Point A is at

(6, 1)

and point C is at

(2, -7)

.
Find the coordinates of point B on

\overline{AC}

such that

AB = \frac{1}{3}BC

.

Find the following trigonometric value:

\sin(30°)

Express your answer exactly.

A

26

‑foot ladder leans against a vertical wall. The base of the ladder is

10

feet from the wall.
How high up the wall does the ladder reach?

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